Programming with Less Than Nothing

Dana. The interviewer. Friendly, efficient. She leans forward. “So,” she says, “walk me through FizzBuzz.” You could do this in your sleep. “Is JavaScript okay?” She nods. You open your laptop and begin. let S = ( x ) => ( y ) => ( z ) => x ( z )( y ( z )); let K = ( x ) => ( y ) => x ; “That should do it,” you say to yourself. “Just need to combine these a few times.” Dana raises an eyebrow. You continue. let I = S ( K )( K ); // x => x let B = S ( K ( S ))( K ); // x => y => z => x(y(z)) let C = S ( B ( B )( S ))( K ( K )); // x => y => z => x(z)(y) let W = S ( S )( K ( I )); // x => y => x(y)(y) let T = C ( I ); // x => y => y(x) Bluebird, cardinal, warbler, thrush. Avian friends you know well. Dana looks puzzled. “Are we still doing FizzBuzz?” “Getting there.” let V = B ( C )( T ); // x => y => z => z(x)(y) let R = B ( B )( T ); // x => y => z => y(z)(x) let B1 = B ( B )( B ); // x => y => z => w => x(y)(z)(w) let E = B ( B1 ); // x => y => z => w => v => x(y)(z(w(v))) let C_STAR = B ( C ); // x => y => z => w => x(y)(w)(z) let C_STAR_STAR = B ( C_STAR ); // x => y => z => w => v => x(y)(z)(v)(w) Dana breaks away from the screen. “Typically I see a for loop by now. Are you sure we’re talking about the same problem?” “Trust me.” let TRUE = K ; let FALSE = K ( I ); let NOT = V ( FALSE )( TRUE ); She stands. “Okay,” she says finally. “Let me stop you there.” “Something wrong?” “You’re not the first candidate to show up here and reinvent programming from first principles using lambda calculus.” You stare, blankly. “Lambda calculus?” “Look,” she says. “We’ve all read Programming with Nothing. We’ve all seen What is PLUS times PLUS. You’re not breaking any new ground here.” You shake your head vigorously. “I would never be caught dead using Lambda calculus. It’s a bloated language.” Dana’s turn to stare. You move on to numbers. let ZERO = I ; let IS_ZERO = T ( TRUE ); let SUCC = V ( FALSE ); // successor let PRED = T ( FALSE ); // predecessor let DECREMENT = S ( W ( IS_ZERO ))( PRED ); // clamped predecessor let ONE = SUCC ( ZERO ); let TWO = SUCC ( ONE ); let THREE = SUCC ( TWO ); let FOUR = SUCC ( THREE ); let FIVE = SUCC ( FOUR ); let SIX = SUCC ( FIVE ); let SEVEN = SUCC ( SIX ); let EIGHT = SUCC ( SEVEN ); let NINE = SUCC ( EIGHT ); let TEN = SUCC ( NINE ); Dana leans forward. She seems interested now. “Church numerals?” “Barendregt. Church is too mainstream.” You start with a lambda calculus expression. let ADD = ( m ) => ( n ) => IS_ZERO ( m )( n )( SUCC ( ADD ( PRED ( m ))( n ))); “Dirty,” you mutter. “But it’s a start.” You scribble in your notepad briefly. Showing all your work would be tedious, but you should at least walk her through the interesting parts. “First, we add combinators until n is by itself on the right.” let ADD = ( m ) => ( n ) => S ( C ( B ( B ( B ))( IS_ZERO )( m ))( SUCC ))( ADD ( PRED ( m )))( n ); “Ah,” she says. “Now we can remove n .” She’s warming up. let ADD = ( m ) => S ( C ( B ( B ( B ))( IS_ZERO )( m ))( SUCC ))( ADD ( PRED ( m ))); You do it again for m // let ADD = (m) => // S(B(S)(C_STAR_STAR(B)(C)(B(B(B))(IS_ZERO))(SUCC)))( // B(ADD)(PRED), // )(m); let ADD = S ( B ( S )( C_STAR_STAR ( B )( C )( B ( B ( B ))( IS_ZERO ))( SUCC )))( B ( ADD )( PRED ), ); Point-free. Clean. But not clean enough. “Now for that pesky self reference…” let ADD_MAKER = ( self ) => S ( B ( S )( C_STAR_STAR ( B )( C )( B ( B ( B ))( IS_ZERO ))( SUCC )))( B ( self )( PRED ), ); let Y = W ( C )( S ( B )( C ( W ( C )))); // x => (y => x(y(y)))(y => x(y(y))) “Is that the… Y combinator?” Dana asks. “Can’t recurse without it.” “It’s JavaScript. You can literally do recursion without it.” “It won’t be JavaScript for much longer.” let ADD = Y ( ADD_MAKER ); console . log ( ADD ( ONE )( TWO )); You run the program for the first time. Uncaught RangeError: Maximum call stack size exceeded Dana smirks. “Well, yeah. JavaScript is an eager language. Can’t use the Y combinator.” You saw this coming. You paste your code into Skoobert. “Skoobert?” Dana asks. “JavaScript but lazy,” you explain. “And without the bloat.” You run it again. [Function] You sigh. Perfect code tarnished by human consumption. let extractNumber = Y ( B ( S ( C ( IS_ZERO )( 0 )))( B ( B (( x ) => x + 1 ))( C ( B )( PRED ))), ); console . log ( extractNumber ( ADD ( ONE )( TWO ))); 3 Back on track. You type faster. let SUBTRACT = C ( Y ( B ( S ( B ( S )( C_STAR_STAR ( B )( C )( B ( B ( B ))( IS_ZERO ))( DECREMENT ))))( C ( S ( K ( I ))( B ))( PRED ), ), ), ); let MULTIPLY = Y ( B ( C )( B ( S ( B ( B )( C ( IS_ZERO )( ZERO ))))( B ( B ( S ( ADD )))( C ( B ( B )( C ))( PRED )), ), ), ); let LESS_THAN_OR_EQUAL = B1 ( IS_ZERO )( SUBTRACT ); let GREATER_THAN_OR_EQUAL = C ( LESS_THAN_OR_EQUAL ); let GREATER_THAN = B1 ( NOT )( LESS_THAN_OR_EQUAL ); let LESS_THAN = B1 ( NOT )( GREATER_THAN_OR_EQUAL ); let RECURSE_SUB = B ( B ( W ))( C ( B ( B )( B ))( SUBTRACT )); let MOD = Y ( B ( S ( B ( S )( W ( C_STAR ( LESS_THAN )))))( RECURSE_SUB )); let DIVIDE = Y ( B ( B ( S ( C ( IS_ZERO )( ZERO ))))( B ( S ( B ( S )( C ( B ( C )( LESS_THAN ))( ZERO ))))( B ( B ( B ( SUCC )))( RECURSE_SUB ), ), ), ); Numbers are done. Lists: let CONS = V ; let FIRST = T ( TRUE ); let REST = T ( FALSE ); let EMPTY = K ( TRUE ); let END = EMPTY ; let IS_EMPTY = T ( K ( K ( FALSE ))); let NTH = Y ( B ( S ( B ( S )( B ( C ( IS_ZERO ))( FIRST ))))( C ( B ( C )( B ( B ( B ))( C ( B )( REST ))))( PRED ), ), ); let CONCAT = B ( T ( CONS ))( FOLD ); let RANGE = Y ( C ( B ( C )( B ( B ( C ))( B ( S ( B ( S )( LESS_THAN_OR_EQUAL )))( B ( S ( B ( B )( CONS )))( C ( B )( SUCC )), ), ), ), )( EMPTY ), ); let FOLD = Y ( B ( S ( B ( B )( B ( S )( IS_EMPTY ))))( B ( S ( B ( S )( C ( B ( B ( B ))( C ( B )( FIRST ))))))( C ( B )( REST )), ), ); let MAP = C ( B ( C )( C ( B ( B )( FOLD ))( B ( CONS ))))( EMPTY ); More pretty-printing: let renderList = ( fmt ) => ( sep ) => ( xs ) => IS_EMPTY ( xs )( "" )( fmt ( FIRST ( xs )) + IS_EMPTY ( REST ( xs ))( "" )( sep + renderList ( fmt )( sep )( REST ( xs )), ), ); let showLines = ( fmt ) => ( list ) => renderList ( fmt )( " " )( list ); “I won’t bother making the formatters point-free, since they’re just output,” you say, as if Dana cares. Sanity check: console . log ( showLines ( extractNumber )( MAP ( RANGE ( ONE )( THREE ))( SUCC )), ); 2 3 4 Dana has given up following along. let DECIMAL2 = B ( ADD )( MULTIPLY ( TEN )); // base 10 let CHAR_A = ONE ; let CHAR_B = TWO ; let CHAR_C = THREE ; let CHAR_D = FOUR ; let CHAR_E = FIVE ; let CHAR_F = SIX ; let CHAR_G = SEVEN ; let CHAR_H = EIGHT ; let CHAR_I = NINE ; let CHAR_J = TEN ; let CHAR_K = DECIMAL2 ( ONE )( ONE ); let CHAR_L = DECIMAL2 ( ONE )( TWO ); let CHAR_M = DECIMAL2 ( ONE )( THREE ); let CHAR_N = DECIMAL2 ( ONE )( FOUR ); let CHAR_O = DECIMAL2 ( ONE )( FIVE ); let CHAR_P = DECIMAL2 ( ONE )( SIX ); let CHAR_Q = DECIMAL2 ( ONE )( SEVEN ); let CHAR_R = DECIMAL2 ( ONE )( EIGHT ); let CHAR_S = DECIMAL2 ( ONE )( NINE ); let CHAR_T = DECIMAL2 ( TWO )( ZERO ); let CHAR_U = DECIMAL2 ( TWO )( ONE ); let CHAR_V = DECIMAL2 ( TWO )( TWO ); let CHAR_W = DECIMAL2 ( TWO )( THREE ); let CHAR_X = DECIMAL2 ( TWO )( FOUR ); let CHAR_Y = DECIMAL2 ( TWO )( FIVE ); let CHAR_Z = DECIMAL2 ( TWO )( SIX ); let CHAR_0 = DECIMAL2 ( TWO )( SEVEN ); let CHAR_1 = DECIMAL2 ( TWO )( EIGHT ); let CHAR_2 = DECIMAL2 ( TWO )( NINE ); let CHAR_3 = DECIMAL2 ( THREE )( ZERO ); let CHAR_4 = DECIMAL2 ( THREE )( ONE ); let CHAR_5 = DECIMAL2 ( THREE )( TWO ); let CHAR_6 = DECIMAL2 ( THREE )( THREE ); let CHAR_7 = DECIMAL2 ( THREE )( FOUR ); let CHAR_8 = DECIMAL2 ( THREE )( FIVE ); let CHAR_9 = DECIMAL2 ( THREE )( SIX ); let ARRAY = Y ( B ( S ( B ( S )( C ( B ( C ( IS_EMPTY )))( END ))))( C ( B ( B )( B ))( C ( B ( B )( B ))( CONS )), ), )( I ); let FIZZ = ARRAY ( CHAR_F )( CHAR_I )( CHAR_Z )( CHAR_Z )( END ); let BUZZ = ARRAY ( CHAR_B )( CHAR_U )( CHAR_Z )( CHAR_Z )( END ); let FIZZBUZZ = CONCAT ( FIZZ )( BUZZ ); Printing strings: let extractString = ( lst ) => IS_EMPTY ( lst )( "" )( NTH ( letters )( PRED ( FIRST ( lst ))) + extractString ( REST ( lst )), ); console . log ( extractString ( FIZZBUZZ )); fizzbuzz Just a few more loose ends. Numbers to digits. Digits to strings. Strings to output. let array = Y ( ( h ) => ( acc ) => ( x ) => x === END ? acc ( END ) : h (( t ) => acc ( CONS ( x )( t ))), )( I ); let letters = array ( "a" )( "b" )( "c" )( "d" )( "e" )( "f" )( "g" )( "h" )( "i" )( "j" ) ( "k" )( "l" )( "m" )( "n" )( "o" )( "p" )( "q" )( "r" )( "s" )( "t" )( "u" ) ( "v" )( "w" )( "x" )( "y" )( "z" ) ( "0" )( "1" )( "2" )( "3" )( "4" )( "5" )( "6" )( "7" )( "8" )( "9" )( END ); let DIGITS_NUMERAL = ARRAY ( CHAR_0 )( CHAR_1 )( CHAR_2 )( CHAR_3 )( CHAR_4 ) ( CHAR_5 )( CHAR_6 )( CHAR_7 )( CHAR_8 )( CHAR_9 )( END ); let NUMBER_TO_DIGIT_LIST = Y ( C ( B ( S )( C ( B ( B )( B ( S ( B ( S )( IS_ZERO )))( B ( CONCAT ))))( C ( DIVIDE )( TEN )), ), )( C ( B ( CONS )( C ( MOD )( TEN )))( EMPTY )), ); let NUMBER_TO_STRING = S ( C ( B ( FOLD )( NUMBER_TO_DIGIT_LIST ))( B ( CONS )( NTH ( DIGITS_NUMERAL )), ), )( B ( T ( EMPTY ))( K ( I ))); You take a deep breath and look Dana in the eye. “And now… the main event.” let FIFTEEN = DECIMAL2 ( ONE )( FIVE ); let ONE_HUNDRED = MULTIPLY ( TEN )( TEN ); let FIZZBUZZ_RESULT = MAP ( RANGE ( ONE )( ONE_HUNDRED ))( S ( B ( S ( C ( R ( FIZZBUZZ ))( FIFTEEN )))( B ( S ( C ( R ( FIZZ ))( THREE )))( B ( C ( C ( R ( BUZZ ))( FIVE )))( NUMBER_TO_STRING ), ), ), )( B ( B ( IS_ZERO ))( MOD )), ); console . log ( showLines ( extractString )( FIZZBUZZ_RESULT )); “Are you satisfied?” she cries. But you aren’t. Not yet. Variables are for wimps. You replace each with its definition. let FIZZBUZZ_RESULT = (((((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((((( S )(( K )( S )))( K ))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K ))))((((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))(((((( S )( S ))(( K )((( S )( K ))( K ))))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K ))))((( S )((( S )(( K )( S )))( K )))(((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))(((( S )( S ))(( K )((( S )( K ))( K ))))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))))))((((( S )(( K )( S )))( K ))(( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))((((( S )(( K )( S )))( K ))( S ))((((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )( K ))( K )))(( K )(( K )(( K )((( S )( K ))( K ))))))))))((((( S )(( K )( S )))( K ))(( S )((((( S )(( K )( S )))( K ))( S ))(((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((((( S )(( K )( S )))( K ))(((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K ))))((((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )(( K )( S )))( K )))((((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )( K ))( K )))( K ))))))))((((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )(( K )( S )))( K )))((((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )( K ))( K )))(( K )((( S )( K ))( K ))))))))))(((( S )(( K )( S )))( K ))((((( S )(( K )( S )))( K ))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K ))))(((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )( K ))( K ))))))))(( K )( K )))(((((((( S )( S ))(( K )((( S )( K ))( K ))))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K ))))((( S )((( S )(( K )( S )))( K )))(((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))(((( S )( S ))(( K )((( S )( K ))( K ))))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))))))((((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((((( S )(( K )( S )))( K ))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K ))))((((( S )(( K )( S )))( K ))(((( S )(( K )( S )))( K ))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))))((((( S )(( K )( S )))( K ))(( S )((((( S )(( K )( S )))( K ))( S ))((((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))((( S )(( K )( S )))( K )))((((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )( K ))( K )))( K )))(((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))(((((( S )( S ))(( K )((( S )( K ))( K ))))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K ))))((( S )((( S )(( K )( S )))( K )))(((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))(((( S )( S ))(( K )((( S )( K ))( K ))))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))))))((((( S )(( K )( S )))( K ))(( S )((((( S )(( K )( S )))( K ))( S ))(((((((( S )(( K )( S )))( K ))(((( S )(( K )( S )))( K ))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))))((( S )(( K )( S )))( K )))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K ))))((((( S )(( K )( S )))( K ))(((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K ))))((((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )( K ))( K )))( K ))))((( S )(((( S )( S ))(( K )((( S )( K ))( K ))))((((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )( K ))( K )))( K ))))((((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )( K ))( K )))(( K )((( S )( K ))( K )))))))))((((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )(( K )((( S )( K ))( K ))))((( S )(( K )( S )))( K ))))((((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )( K ))( K )))(( K )((( S )( K ))( K ))))))))))))((((( S )(( K )( S )))( K ))(( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))((((( S )(( K )( S )))( K ))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K ))))(((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )( K ))( K )))))))((((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )(( K )( S )))( K )))(((((( S )(( K )( S )))( K ))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K ))))(((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )( K ))( K ))))(( K )((( S )( K ))( K ))))))))))(( K )( K ))))((((((( S )(( K )( S )))( K ))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K ))))(((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )( K ))( K ))))(( K )((( S )( K ))( K ))))((( S )( K ))( K ))))(((((((( S )( S ))(( K )((( S )( K ))( K ))))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K ))))((( S )((( S )(( K )( S )))( K )))(((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))(((( S )( S ))(( K )((( S )( K ))( K ))))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))))))((((( S )(( K )( S )))( K ))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K ))))((((( S )(( K )( S )))( K ))(( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))((((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )( K ))( K )))( K )))((( S )( K ))( K ))))))((((( S )(( K )( S )))( K ))(((( S )(( K )( S )))( K ))(( S )(((((( S )( S ))(( K )((( S )( K ))( K ))))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K ))))((( S )((( S )(( K )( S )))( K )))(((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))(((( S )( S ))(( K )((( S )( K ))( K ))))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))))))((((( S )(( K )( S )))( K ))(( S )((((( S )(( K )( S )))( K ))( S ))(((((((( S )(( K )( S )))( K ))(((( S )(( K )( S )))( K ))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))))((( S )(( K )( S )))( K )))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K ))))((((( S )(( K )( S )))( K ))(((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K ))))((((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )( K ))( K )))( K ))))(((((( S )(( K )( S )))( K ))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K ))))(((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )( K ))( K ))))(( K )((( S )( K ))( K ))))))))((((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )(( K )((( S )( K ))( K ))))((( S )(( K )( S )))( K ))))((((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )( K ))( K )))(( K )((( S )( K ))( K ))))))))))((((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))))((((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )( K ))( K )))(( K )((( S )( K ))( K )))))))))((((((( S )(( K )( S )))( K ))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K ))))(((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )( K ))( K ))))(( K )((( S )( K ))( K ))))((((((( S )(( K )( S )))( K ))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K ))))(((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )( K ))( K ))))(( K )((( S )( K ))( K ))))((((((( S )(( K )( S )))( K ))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K ))))(((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )( K ))( K ))))(( K )((( S )( K ))( K ))))((((((( S )(( K )( S )))( K ))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K ))))(((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )( K ))( K ))))(( K )((( S )( K ))( K ))))((((((( S )(( K )( S )))( K ))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K ))))(((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )( K ))( K ))))(( K )((( S )( K ))( K ))))((((((( S )(( K )( S )))( K ))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K ))))(((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )( K ))( K ))))(( K )((( S )( K ))( K ))))((((((( S )(( K )( S )))( K ))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K ))))(((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )( K ))( K ))))(( K )((( S )( K ))( K ))))((((((( S )(( K )( S )))( K ))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K ))))(((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )( K ))( K ))))(( K )((( S )( K ))( K ))))((((((( S )(( K )( S )))( K ))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K ))))(((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )( K ))( K ))))(( K )((( S )( K ))( K ))))((((((( S )(( K )( S )))( K ))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K ))))(((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )( K ))( K ))))(( K )((( S )( K ))( K ))))((( S )( K ))( K )))))))))))))((((((( S )(( K )( S )))( K ))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K ))))(((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )( K ))( K ))))(( K )((( S )( K ))( K ))))((((((( S )(( K )( S )))( K ))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K ))))(((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )( K ))( K ))))(( K )((( S )( K ))( K ))))((((((( S )(( K )( S )))( K ))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K ))))(((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )( K ))( K ))))(( K )((( S )( K ))( K ))))((((((( S )(( K )( S )))( K ))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K ))))(((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )( K ))( K ))))(( K )((( S )( K ))( K ))))((((((( S )(( K )( S )))( K ))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K ))))(((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )( K ))( K ))))(( K )((( S )( K ))( K ))))((((((( S )(( K )( S )))( K ))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K ))))(((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )( K ))( K ))))(( K )((( S )( K ))( K ))))((((((( S )(( K )( S )))( K ))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K ))))(((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )( K ))( K ))))(( K )((( S )( K ))( K ))))((((((( S )(( K )( S )))( K ))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K ))))(((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )( K ))( K ))))(( K )((( S )( K ))( K ))))((((((( S )(( K )( S )))( K ))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K ))))(((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )( K ))( K ))))(( K )((( S )( K ))( K ))))((((((( S )(( K )( S )))( K ))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K ))))(((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )( K ))( K ))))(( K )((( S )( K ))( K ))))((( S )( K ))( K )))))))))))))))((( S )((((( S )(( K )( S )))( K ))(( S )((((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))(((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))(((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )( K ))( K ))))((((((( S )(( K )( S )))( K ))((((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )( K ))( K )))((((( S )(( K )( S )))( K ))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K ))))(((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )( K ))( K ))))))(((((( S )( S ))(( K )((( S )( K ))( K ))))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K ))))((( S )((( S )(( K )( S )))( K )))(((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))(((( S )( S ))(( K )((( S )( K ))( K ))))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))))))((((( S )(( K )( S )))( K ))(( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))((((( S )(( K )( S )))( K ))( S ))((((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )( K ))( K )))(( K )(( K )(( K )((( S )( K ))( K ))))))))))((((( S )(( K )( S )))( K ))(( S )((((( S )(( K )( S )))( K ))( S ))(((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((((( S )(( K )( S )))( K ))(((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K ))))((((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )(( K )( S )))( K )))((((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )( K ))( K )))( K ))))))))((((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )(( K )( S )))( K )))((((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )( K ))( K )))(( K )((( S )( K ))( K )))))))))(((((((((((( S )( S ))(( K )((( S )( K ))( K ))))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K ))))((( S )((( S )(( K )( S )))( K )))(((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))(((( S )( S ))(( K )((( S )( K ))( K ))))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))))))((((( S )(( K )( S )))( K ))(( S )((((( S )(( K )( S )))( K ))( S ))((((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))(((( S )(( K )( S )))( K ))(((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )( K ))( K )))(( K )(( K )(( K )((( S )( K ))( K )))))))))(( K )( K ))))))((((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))((( S )(( K )( S )))( K ))))((((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))((( S )(( K )( S )))( K ))))((((( S )(( K )( S )))( K ))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K ))))(((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )( K ))( K ))))))))((( S )( K ))( K )))((((((( S )(( K )( S )))( K ))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K ))))(((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )( K ))( K ))))(( K )((( S )( K ))( K ))))((((((( S )(( K )( S )))( K ))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K ))))(((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )( K ))( K ))))(( K )((( S )( K ))( K ))))((((((( S )(( K )( S )))( K ))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K ))))(((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )( K ))( K ))))(( K )((( S )( K ))( K ))))((((((( S )(( K )( S )))( K ))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K ))))(((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )( K ))( K ))))(( K )((( S )( K ))( K ))))((((((( S )(( K )( S )))( K ))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K ))))(((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )( K ))( K ))))(( K )((( S )( K ))( K ))))((((((( S )(( K )( S )))( K ))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K ))))(((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )( K ))( K ))))(( K )((( S )( K ))( K ))))((( S )( K ))( K )))))))))((((((( S )(( K )( S )))( K ))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K ))))(((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )( K ))( K ))))(( K )((( S )( K ))( K ))))((((((( S )(( K )( S )))( K ))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K ))))(((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )( K ))( K ))))(( K )((( S )( K ))( K ))))((((((( S )(( K )( S )))( K ))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K ))))(((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )( K ))( K ))))(( K )((( S )( K ))( K ))))((((((( S )(( K )( S )))( K ))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K ))))(((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )( K ))( K ))))(( K )((( S )( K ))( K ))))((((((( S )(( K )( S )))( K ))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K ))))(((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )( K ))( K ))))(( K )((( S )( K ))( K ))))((((((( S )(( K )( S )))( K ))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K ))))(((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )( K ))( K ))))(( K )((( S )( K ))( K ))))((((((( S )(( K )( S )))( K ))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K ))))(((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )( K ))( K ))))(( K )((( S )( K ))( K ))))((((((( S )(( K )( S )))( K ))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K ))))(((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )( K ))( K ))))(( K )((( S )( K ))( K ))))((((((( S )(( K )( S )))( K ))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K ))))(((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )( K ))( K ))))(( K )((( S )( K ))( K ))))((( S )( K ))( K ))))))))))))((((((( S )(( K )( S )))( K ))(((((( S )( S ))(( K )((( S )( K ))( K ))))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K ))))((( S )((( S )(( K )( S )))( K )))(((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))(((( S )( S ))(( K )((( S )( K ))( K ))))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))))))((((( S )(( K )( S )))( K ))(( S )((((( S )(( K )( S )))( K ))( S ))(((((((( S )(( K )( S )))( K ))(((( S )(( K )( S )))( K ))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))))((( S )(( K )( S )))( K )))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K ))))((((( S )(( K )( S )))( K ))(((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K ))))((((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )( K ))( K )))( K ))))(((((( S )(( K )( S )))( K ))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K ))))(((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )( K ))( K ))))(( K )((( S )( K ))( K ))))))))((((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )(( K )((( S )( K ))( K ))))((( S )(( K )( S )))( K ))))((((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )( K ))( K )))(( K )((( S )( K ))( K ))))))))((((((( S )( S ))(( K )((( S )( K ))( K ))))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K ))))((( S )((( S )(( K )( S )))( K )))(((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))(((( S )( S ))(( K )((( S )( K ))( K ))))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))))))((((( S )(( K )( S )))( K ))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K ))))((((( S )(( K )( S )))( K ))(( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))((((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )( K ))( K )))( K )))((( S )( K ))( K ))))))((((( S )(( K )( S )))( K ))(((( S )(( K )( S )))( K ))(( S )(((((( S )( S ))(( K )((( S )( K ))( K ))))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K ))))((( S )((( S )(( K )( S )))( K )))(((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))(((( S )( S ))(( K )((( S )( K ))( K ))))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))))))((((( S )(( K )( S )))( K ))(( S )((((( S )(( K )( S )))( K ))( S ))(((((((( S )(( K )( S )))( K ))(((( S )(( K )( S )))( K ))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))))((( S )(( K )( S )))( K )))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K ))))((((( S )(( K )( S )))( K ))(((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K ))))((((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )( K ))( K )))( K ))))(((((( S )(( K )( S )))( K ))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K ))))(((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )( K ))( K ))))(( K )((( S )( K ))( K ))))))))((((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )(( K )((( S )( K ))( K ))))((( S )(( K )( S )))( K ))))((((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )( K ))( K )))(( K )((( S )( K ))( K ))))))))))((((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))))((((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )( K ))( K )))(( K )((( S )( K ))( K )))))))))((((((( S )(( K )( S )))( K ))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K ))))(((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))(( K )( K )))((( S )( K ))( K ))))(( K )((( S )( K ))( K ))))((((((( S )(( K )( S )))( K ))((( S )((((( S )(( K )( S )))( K ))((( S )(( K )( S )))( K )))( S )))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((S)(K))(K))))))))))))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((S)(K))(K)))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((S)(K))(K))))))))))(((((((S)((K)(S)))(K))((((((S)(S))((K)(((S)(K))(K))))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))(((S)(((S)((K)(S)))(K)))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))((((S)(S))((K)(((S)(K))(K))))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))))))(((((S)((K)(S)))(K))((S)(((((S)((K)(S)))(K))(S))((((((((S)((K)(S)))(K))((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))))(((S)((K)(S)))(K)))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))(((((S)((K)(S)))(K))((((S)((K)(S)))(K))(((S)((K)(S)))(K))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K)))(K))))((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)((K)(((S)(K))(K))))(((S)((K)(S)))(K))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K)))((K)(((S)(K))(K))))))))(((((((S)(S))((K)(((S)(K))(K))))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))(((S)(((S)((K)(S)))(K)))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))((((S)(S))((K)(((S)(K))(K))))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))))))(((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))(((((S)((K)(S)))(K))((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K)))(K)))(((S)(K))(K))))))(((((S)((K)(S)))(K))((((S)((K)(S)))(K))((S)((((((S)(S))((K)(((S)(K))(K))))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))(((S)(((S)((K)(S)))(K)))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))((((S)(S))((K)(((S)(K))(K))))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))))))(((((S)((K)(S)))(K))((S)(((((S)((K)(S)))(K))(S))((((((((S)((K)(S)))(K))((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))))(((S)((K)(S)))(K)))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))(((((S)((K)(S)))(K))((((S)((K)(S)))(K))(((S)((K)(S)))(K))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K)))(K))))((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)((K)(((S)(K))(K))))(((S)((K)(S)))(K))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K)))((K)(((S)(K))(K))))))))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K)))((K)(((S)(K))(K)))))))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((S)(K))(K))))))))))))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((S)(K))(K)))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((S)(K))(K))))))))))((K)(K))))((((((((((((S)(S))((K)(((S)(K))(K))))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))(((S)(((S)((K)(S)))(K)))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))((((S)(S))((K)(((S)(K))(K))))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))))))(((((S)((K)(S)))(K))((S)(((((S)((K)(S)))(K))(S))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))((((S)((K)(S)))(K))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K)))((K)((K)((K)(((S)(K))(K)))))))))((K)(K))))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(((S)((K)(S)))(K))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(((S)((K)(S)))(K))))(((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))))))(((S)(K))(K)))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((S)(K))(K)))))(((((((S)((K)(S)))(K))((((((S)(S))((K)(((S)(K))(K))))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))(((S)(((S)((K)(S)))(K)))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))((((S)(S))((K)(((S)(K))(K))))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))))))(((((S)((K)(S)))(K))((S)(((((S)((K)(S)))(K))(S))((((((((S)((K)(S)))(K))((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))))(((S)((K)(S)))(K)))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))(((((S)((K)(S)))(K))((((S)((K)(S)))(K))(((S)((K)(S)))(K))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K)))(K))))((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)((K)(((S)(K))(K))))(((S)((K)(S)))(K))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K)))((K)(((S)(K))(K))))))))(((((((S)(S))((K)(((S)(K))(K))))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))(((S)(((S)((K)(S)))(K)))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))((((S)(S))((K)(((S)(K))(K))))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))))))(((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))(((((S)((K)(S)))(K))((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K)))(K)))(((S)(K))(K))))))(((((S)((K)(S)))(K))((((S)((K)(S)))(K))((S)((((((S)(S))((K)(((S)(K))(K))))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))(((S)(((S)((K)(S)))(K)))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))((((S)(S))((K)(((S)(K))(K))))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))))))(((((S)((K)(S)))(K))((S)(((((S)((K)(S)))(K))(S))((((((((S)((K)(S)))(K))((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))))(((S)((K)(S)))(K)))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))(((((S)((K)(S)))(K))((((S)((K)(S)))(K))(((S)((K)(S)))(K))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K)))(K))))((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)((K)(((S)(K))(K))))(((S)((K)(S)))(K))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K)))((K)(((S)(K))(K))))))))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K)))((K)(((S)(K))(K)))))))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((S)(K))(K))))))))))))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((S)(K))(K)))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((S)(K))(K)))))(((((((S)((K)(S)))(K))((((((S)(S))((K)(((S)(K))(K))))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))(((S)(((S)((K)(S)))(K)))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))((((S)(S))((K)(((S)(K))(K))))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))))))(((((S)((K)(S)))(K))((S)(((((S)((K)(S)))(K))(S))((((((((S)((K)(S)))(K))((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))))(((S)((K)(S)))(K)))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))(((((S)((K)(S)))(K))((((S)((K)(S)))(K))(((S)((K)(S)))(K))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K)))(K))))((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)((K)(((S)(K))(K))))(((S)((K)(S)))(K))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K)))((K)(((S)(K))(K))))))))(((((((S)(S))((K)(((S)(K))(K))))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))(((S)(((S)((K)(S)))(K)))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))((((S)(S))((K)(((S)(K))(K))))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))))))(((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))(((((S)((K)(S)))(K))((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K)))(K)))(((S)(K))(K))))))(((((S)((K)(S)))(K))((((S)((K)(S)))(K))((S)((((((S)(S))((K)(((S)(K))(K))))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))(((S)(((S)((K)(S)))(K)))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))((((S)(S))((K)(((S)(K))(K))))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))))))(((((S)((K)(S)))(K))((S)(((((S)((K)(S)))(K))(S))((((((((S)((K)(S)))(K))((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))))(((S)((K)(S)))(K)))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))(((((S)((K)(S)))(K))((((S)((K)(S)))(K))(((S)((K)(S)))(K))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K)))(K))))((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)((K)(((S)(K))(K))))(((S)((K)(S)))(K))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K)))((K)(((S)(K))(K))))))))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K)))((K)(((S)(K))(K)))))))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((S)(K))(K))))))))))))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((S)(K))(K)))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((S)(K))(K))))))))))(((((((S)((K)(S)))(K))((((((S)(S))((K)(((S)(K))(K))))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))(((S)(((S)((K)(S)))(K)))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))((((S)(S))((K)(((S)(K))(K))))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))))))(((((S)((K)(S)))(K))((S)(((((S)((K)(S)))(K))(S))((((((((S)((K)(S)))(K))((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))))(((S)((K)(S)))(K)))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))(((((S)((K)(S)))(K))((((S)((K)(S)))(K))(((S)((K)(S)))(K))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K)))(K))))((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)((K)(((S)(K))(K))))(((S)((K)(S)))(K))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K)))((K)(((S)(K))(K))))))))(((((((S)(S))((K)(((S)(K))(K))))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))(((S)(((S)((K)(S)))(K)))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))((((S)(S))((K)(((S)(K))(K))))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))))))(((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))(((((S)((K)(S)))(K))((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K)))(K)))(((S)(K))(K))))))(((((S)((K)(S)))(K))((((S)((K)(S)))(K))((S)((((((S)(S))((K)(((S)(K))(K))))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))(((S)(((S)((K)(S)))(K)))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))((((S)(S))((K)(((S)(K))(K))))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))))))(((((S)((K)(S)))(K))((S)(((((S)((K)(S)))(K))(S))((((((((S)((K)(S)))(K))((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))))(((S)((K)(S)))(K)))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))(((((S)((K)(S)))(K))((((S)((K)(S)))(K))(((S)((K)(S)))(K))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K)))(K))))((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)((K)(((S)(K))(K))))(((S)((K)(S)))(K))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K)))((K)(((S)(K))(K))))))))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K)))((K)(((S)(K))(K)))))))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((S)(K))(K))))))))))))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((S)(K))(K)))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((S)(K))(K))))))))))((K)(K))))))(((((((S)((K)(S)))(K))((((((S)(S))((K)(((S)(K))(K))))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))(((S)(((S)((K)(S)))(K)))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))((((S)(S))((K)(((S)(K))(K))))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))))))(((((S)((K)(S)))(K))((S)(((((S)((K)(S)))(K))(S))((((((((S)((K)(S)))(K))((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))))(((S)((K)(S)))(K)))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))(((((S)((K)(S)))(K))((((S)((K)(S)))(K))(((S)((K)(S)))(K))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K)))(K))))((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)((K)(((S)(K))(K))))(((S)((K)(S)))(K))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K)))((K)(((S)(K))(K))))))))(((((((S)(S))((K)(((S)(K))(K))))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))(((S)(((S)((K)(S)))(K)))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))((((S)(S))((K)(((S)(K))(K))))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))))))(((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))(((((S)((K)(S)))(K))((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K)))(K)))(((S)(K))(K))))))(((((S)((K)(S)))(K))((((S)((K)(S)))(K))((S)((((((S)(S))((K)(((S)(K))(K))))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))(((S)(((S)((K)(S)))(K)))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))((((S)(S))((K)(((S)(K))(K))))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))))))(((((S)((K)(S)))(K))((S)(((((S)((K)(S)))(K))(S))((((((((S)((K)(S)))(K))((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))))(((S)((K)(S)))(K)))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))(((((S)((K)(S)))(K))((((S)((K)(S)))(K))(((S)((K)(S)))(K))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K)))(K))))((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)((K)(((S)(K))(K))))(((S)((K)(S)))(K))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K)))((K)(((S)(K))(K))))))))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K)))((K)(((S)(K))(K)))))))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((S)(K))(K))))))))))))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((S)(K))(K)))))))))))(((((S)((K)(S)))(K))((S)(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))((((((S)((K)(S)))(K))(((S)((K)(S)))(K)))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((((((((((((S)(S))((K)(((S)(K))(K))))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))(((S)(((S)((K)(S)))(K)))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))((((S)(S))((K)(((S)(K))(K))))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))))))(((((S)((K)(S)))(K))((S)(((((S)((K)(S)))(K))(S))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))((((S)((K)(S)))(K))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K)))((K)((K)((K)(((S)(K))(K)))))))))((K)(K))))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(((S)((K)(S)))(K))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(((S)((K)(S)))(K))))(((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))))))(((S)(K))(K)))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((S)(K))(K)))))))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((S)(K))(K))))))))))))(((((((S)((K)(S)))(K))((((((S)(S))((K)(((S)(K))(K))))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))(((S)(((S)((K)(S)))(K)))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))((((S)(S))((K)(((S)(K))(K))))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))))))(((((S)((K)(S)))(K))((S)(((((S)((K)(S)))(K))(S))((((((((S)((K)(S)))(K))((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))))(((S)((K)(S)))(K)))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))(((((S)((K)(S)))(K))((((S)((K)(S)))(K))(((S)((K)(S)))(K))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K)))(K))))((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)((K)(((S)(K))(K))))(((S)((K)(S)))(K))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K)))((K)(((S)(K))(K))))))))(((((((S)(S))((K)(((S)(K))(K))))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))(((S)(((S)((K)(S)))(K)))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))((((S)(S))((K)(((S)(K))(K))))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))))))(((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))(((((S)((K)(S)))(K))((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K)))(K)))(((S)(K))(K))))))(((((S)((K)(S)))(K))((((S)((K)(S)))(K))((S)((((((S)(S))((K)(((S)(K))(K))))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))(((S)(((S)((K)(S)))(K)))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))((((S)(S))((K)(((S)(K))(K))))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))))))(((((S)((K)(S)))(K))((S)(((((S)((K)(S)))(K))(S))((((((((S)((K)(S)))(K))((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))))(((S)((K)(S)))(K)))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))(((((S)((K)(S)))(K))((((S)((K)(S)))(K))(((S)((K)(S)))(K))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K)))(K))))((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)((K)(((S)(K))(K))))(((S)((K)(S)))(K))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K)))((K)(((S)(K))(K))))))))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K)))((K)(((S)(K))(K)))))))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((S)(K))(K))))))))))))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((S)(K))(K)))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((S)(K))(K))))))))))(((((((S)((K)(S)))(K))((((((S)(S))((K)(((S)(K))(K))))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))(((S)(((S)((K)(S)))(K)))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))((((S)(S))((K)(((S)(K))(K))))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))))))(((((S)((K)(S)))(K))((S)(((((S)((K)(S)))(K))(S))((((((((S)((K)(S)))(K))((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))))(((S)((K)(S)))(K)))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))(((((S)((K)(S)))(K))((((S)((K)(S)))(K))(((S)((K)(S)))(K))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K)))(K))))((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)((K)(((S)(K))(K))))(((S)((K)(S)))(K))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K)))((K)(((S)(K))(K))))))))(((((((S)(S))((K)(((S)(K))(K))))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))(((S)(((S)((K)(S)))(K)))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))((((S)(S))((K)(((S)(K))(K))))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))))))(((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))(((((S)((K)(S)))(K))((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K)))(K)))(((S)(K))(K))))))(((((S)((K)(S)))(K))((((S)((K)(S)))(K))((S)((((((S)(S))((K)(((S)(K))(K))))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))(((S)(((S)((K)(S)))(K)))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))((((S)(S))((K)(((S)(K))(K))))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))))))(((((S)((K)(S)))(K))((S)(((((S)((K)(S)))(K))(S))((((((((S)((K)(S)))(K))((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))))(((S)((K)(S)))(K)))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))(((((S)((K)(S)))(K))((((S)((K)(S)))(K))(((S)((K)(S)))(K))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K)))(K))))((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)((K)(((S)(K))(K))))(((S)((K)(S)))(K))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K)))((K)(((S)(K))(K))))))))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K)))((K)(((S)(K))(K)))))))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((S)(K))(K))))))))))))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((S)(K))(K)))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((S)(K))(K))))))))))((K)(K)))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((S)(K))(K))))))))(((((S)((K)(S)))(K))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))((((((S)((K)(S)))(K))(((S)((K)(S)))(K)))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((((((((((((S)(S))((K)(((S)(K))(K))))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))(((S)(((S)((K)(S)))(K)))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))((((S)(S))((K)(((S)(K))(K))))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))))))(((((S)((K)(S)))(K))((S)(((((S)((K)(S)))(K))(S))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))((((S)((K)(S)))(K))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K)))((K)((K)((K)(((S)(K))(K)))))))))((K)(K))))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(((S)((K)(S)))(K))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(((S)((K)(S)))(K))))(((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))))))(((S)(K))(K)))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((S)(K))(K)))))(((((((S)((K)(S)))(K))((((((S)(S))((K)(((S)(K))(K))))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))(((S)(((S)((K)(S)))(K)))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))((((S)(S))((K)(((S)(K))(K))))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))))))(((((S)((K)(S)))(K))((S)(((((S)((K)(S)))(K))(S))((((((((S)((K)(S)))(K))((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))))(((S)((K)(S)))(K)))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))(((((S)((K)(S)))(K))((((S)((K)(S)))(K))(((S)((K)(S)))(K))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K)))(K))))((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)((K)(((S)(K))(K))))(((S)((K)(S)))(K))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K)))((K)(((S)(K))(K))))))))(((((((S)(S))((K)(((S)(K))(K))))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))(((S)(((S)((K)(S)))(K)))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))((((S)(S))((K)(((S)(K))(K))))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))))))(((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))(((((S)((K)(S)))(K))((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K)))(K)))(((S)(K))(K))))))(((((S)((K)(S)))(K))((((S)((K)(S)))(K))((S)((((((S)(S))((K)(((S)(K))(K))))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))(((S)(((S)((K)(S)))(K)))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))((((S)(S))((K)(((S)(K))(K))))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))))))(((((S)((K)(S)))(K))((S)(((((S)((K)(S)))(K))(S))((((((((S)((K)(S)))(K))((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))))(((S)((K)(S)))(K)))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))(((((S)((K)(S)))(K))((((S)((K)(S)))(K))(((S)((K)(S)))(K))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K)))(K))))((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)((K)(((S)(K))(K))))(((S)((K)(S)))(K))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K)))((K)(((S)(K))(K))))))))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K)))((K)(((S)(K))(K)))))))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((S)(K))(K))))))))))))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((S)(K))(K)))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((S)(K))(K)))))(((((((S)((K)(S)))(K))((((((S)(S))((K)(((S)(K))(K))))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))(((S)(((S)((K)(S)))(K)))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))((((S)(S))((K)(((S)(K))(K))))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))))))(((((S)((K)(S)))(K))((S)(((((S)((K)(S)))(K))(S))((((((((S)((K)(S)))(K))((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))))(((S)((K)(S)))(K)))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))(((((S)((K)(S)))(K))((((S)((K)(S)))(K))(((S)((K)(S)))(K))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K)))(K))))((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)((K)(((S)(K))(K))))(((S)((K)(S)))(K))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K)))((K)(((S)(K))(K))))))))(((((((S)(S))((K)(((S)(K))(K))))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))(((S)(((S)((K)(S)))(K)))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))((((S)(S))((K)(((S)(K))(K))))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))))))(((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))(((((S)((K)(S)))(K))((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K)))(K)))(((S)(K))(K))))))(((((S)((K)(S)))(K))((((S)((K)(S)))(K))((S)((((((S)(S))((K)(((S)(K))(K))))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))(((S)(((S)((K)(S)))(K)))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))((((S)(S))((K)(((S)(K))(K))))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))))))(((((S)((K)(S)))(K))((S)(((((S)((K)(S)))(K))(S))((((((((S)((K)(S)))(K))((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))))(((S)((K)(S)))(K)))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))(((((S)((K)(S)))(K))((((S)((K)(S)))(K))(((S)((K)(S)))(K))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K)))(K))))((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)((K)(((S)(K))(K))))(((S)((K)(S)))(K))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K)))((K)(((S)(K))(K))))))))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K)))((K)(((S)(K))(K)))))))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((S)(K))(K))))))))))))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((S)(K))(K)))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))(((S)(K))(K))))))))))(((((((S)((K)(S)))(K))((((((S)(S))((K)(((S)(K))(K))))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))(((S)(((S)((K)(S)))(K)))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))((((S)(S))((K)(((S)(K))(K))))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))))))(((((S)((K)(S)))(K))((S)(((((S)((K)(S)))(K))(S))((((((((S)((K)(S)))(K))((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))))(((S)((K)(S)))(K)))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))(((((S)((K)(S)))(K))((((S)((K)(S)))(K))(((S)((K)(S)))(K))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K)))(K))))((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)((K)(((S)(K))(K))))(((S)((K)(S)))(K))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K)))((K)(((S)(K))(K))))))))(((((((S)(S))((K)(((S)(K))(K))))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))(((S)(((S)((K)(S)))(K)))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))((((S)(S))((K)(((S)(K))(K))))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))))))(((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))(((((S)((K)(S)))(K))((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K)))(K)))(((S)(K))(K))))))(((((S)((K)(S)))(K))((((S)((K)(S)))(K))((S)((((((S)(S))((K)(((S)(K))(K))))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))(((S)(((S)((K)(S)))(K)))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))((((S)(S))((K)(((S)(K))(K))))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))))))(((((S)((K)(S)))(K))((S)(((((S)((K)(S)))(K))(S))((((((((S)((K)(S)))(K))((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))))(((S)((K)(S)))(K)))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))(((((S)((K)(S)))(K))((((S)((K)(S)))(K))(((S)((K)(S)))(K))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K)))(K))))((((((S)((K)(S)))(K))(((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K))))((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K))))((K)(((S)(K))(K))))))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)((K)(((S)(K))(K))))(((S)((K)(S)))(K))))(((((S)(((((S)((K)(S)))(K))(((S)((K)(S)))(K)))(S)))((K)(K)))(((S)(K))(K)))((K)(((S)(K))(K))))))))))(((((S)(((((S)((K)(S)))