LISP Interpreter Run [omega3.l] [Show that] [ H(Omega_n) > n - 9488.] [Omega_n is the first n bits of Omega,] [where we choose] [ Omega = xxx0111111...] [instead of] [ Omega = xxx1000000...] [if necessary.] [This is an identity function with the size-effect of] [displaying the length in bits of the binary prefix.] define (display-length-of-prefix prefix) cadr cons display length prefix cons prefix nil define display-length-of-prefix value (lambda (prefix) (car (cdr (cons (display (length prefix)) (cons prefix nil))))) cadr try no-time-limit 'eval read-exp [Universal Turing machine U ---] display [--- followed by its program.] append [Append prefix and data.] [Code to display size of prefix in bits.] (display-length-of-prefix bits ' [] [Omega2.l follows.] [] let (count-halt prefix time bits-left-to-extend) if = bits-left-to-extend 0 if = success car try time 'eval read-exp prefix 1 0 + (count-halt append prefix '(0) time - bits-left-to-extend 1) (count-halt append prefix '(1) time - bits-left-to-extend 1) let (omega k) cons (count-halt nil k k) cons / cons ^ 2 k nil [] [Read and execute from remainder of tape] [a program to compute an n-bit] [initial piece of Omega.] [] let w debug eval debug read-exp [] [Convert Omega to ratio of integers,] [i.e., from a bit string to a rational number.] [] let n length w let w debug cons base2-to-10 w cons / cons ^ 2 n nil [] let (loop k) [Main Loop ---] let x debug (omega debug k) [Compute the kth lower bound on Omega.] if debug (<=rat w x) (big nil k n) [Are the first n bits OK? If not, bump k.] (loop + k 1) [If so, form the union of all output of n-bit] [programs within time k, output it, and halt.] [All n-bit programs that ever halt halt by time k.] [Thus this union is bigger than anything of complexity] [less than or equal to n!] [ ] [This total output will be bigger than each individual output,] [and therefore must come from a program with more than n bits.] [Therefore this program itself must be more than n bits long.] [I.e., 9488 + H(Omega_n) > n. Q.E.D.] [] [Compare two rational numbers, i.e., is x= (a / b) <= y= (c / d)?] let (<=rat x y) let a car debug x let b caddr x let c car debug y let d caddr y <= * a d * b c [Union of all output of n-bit programs within time k.] let (big prefix time bits-left-to-add) if = 0 bits-left-to-add try time 'eval read-exp prefix append (big append prefix '(0) time - bits-left-to-add 1) (big append prefix '(1) time - bits-left-to-add 1) (loop 0) [Start main loop running with k = 0.] ) [end of prefix] bits ' [Here is the data: an optimal program to compute n bits of Omega.] '(0 0 0 0 0 0 0 1) [n = 8! Are these really the first 8 bits of Omega?] expression (car (cdr (try no-time-limit (' (eval (read-exp))) (display (append (display-length-of-prefix (bits (' ((' (lambda (count-halt) ((' (lambda (omega) (( ' (lambda (w) ((' (lambda (n) ((' (lambda (w) ((' (lambda (loop) ((' (lambda (<=rat) ((' (lambda (bi g) (loop 0))) (' (lambda (prefix time bits-left-to -add) (if (= 0 bits-left-to-add) (try time (' (eva l (read-exp))) prefix) (append (big (append prefix (' (0))) time (- bits-left-to-add 1)) (big (appen d prefix (' (1))) time (- bits-left-to-add 1)))))) ))) (' (lambda (x y) ((' (lambda (a) ((' (lambda ( b) ((' (lambda (c) ((' (lambda (d) (<= (* a d) (* b c)))) (car (cdr (cdr y)))))) (car (debug y))))) (car (cdr (cdr x)))))) (car (debug x)))))))) (' (l ambda (k) ((' (lambda (x) (if (debug (<=rat w x)) (big nil k n) (loop (+ k 1))))) (debug (omega (deb ug k))))))))) (debug (cons (base2-to-10 w) (cons / (cons (^ 2 n) nil))))))) (length w)))) (debug (ev al (debug (read-exp))))))) (' (lambda (k) (cons (c ount-halt nil k k) (cons / (cons (^ 2 k) nil)))))) )) (' (lambda (prefix time bits-left-to-extend) (i f (= bits-left-to-extend 0) (if (= success (car (t ry time (' (eval (read-exp))) prefix))) 1 0) (+ (c ount-halt (append prefix (' (0))) time (- bits-lef t-to-extend 1)) (count-halt (append prefix (' (1)) ) time (- bits-left-to-extend 1)))))))))) (bits (' (' (0 0 0 0 0 0 0 1))))))))) display 9488 display (0 0 1 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 1 1 0 0 0 1 1 0 0 0 0 1 0 1 1 0 1 1 0 1 0 1 1 0 0 0 1 0 0 1 1 0 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 0 1 1 0 1 1 0 1 1 1 1 0 1 1 1 0 1 0 1 0 1 1 0 1 1 1 0 0 1 1 1 0 1 0 0 0 0 1 0 1 1 0 1 0 1 1 0 1 0 0 0 0 1 1 0 0 0 0 1 0 1 1 0 1 1 0 0 0 1 1 1 0 1 0 0 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 1 1 0 0 0 1 1 0 0 0 0 1 0 1 1 0 1 1 0 1 0 1 1 0 0 0 1 0 0 1 1 0 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 1 1 1 1 0 1 1 0 1 1 0 1 0 1 1 0 0 1 0 1 0 1 1 0 0 1 1 1 0 1 1 0 0 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 1 1 0 0 0 1 1 0 0 0 0 1 0 1 1 0 1 1 0 1 0 1 1 0 0 0 1 0 0 1 1 0 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 1 0 1 1 1 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 1 1 0 0 0 1 1 0 0 0 0 1 0 1 1 0 1 1 0 1 0 1 1 0 0 0 1 0 0 1 1 0 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 1 1 1 0 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 1 1 0 0 0 1 1 0 0 0 0 1 0 1 1 0 1 1 0 1 0 1 1 0 0 0 1 0 0 1 1 0 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 1 0 1 1 1 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 1 1 0 0 0 1 1 0 0 0 0 1 0 1 1 0 1 1 0 1 0 1 1 0 0 0 1 0 0 1 1 0 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 1 1 0 0 0 1 1 0 1 1 1 1 0 1 1 0 1 1 1 1 0 1 1 1 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 1 1 0 0 0 1 1 0 0 0 0 1 0 1 1 0 1 1 0 1 0 1 1 0 0 0 1 0 0 1 1 0 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 1 0 1 1 1 0 0 1 0 0 1 1 0 0 0 0 1 0 1 1 1 0 1 0 0 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 1 1 0 0 0 1 1 0 0 0 0 1 0 1 1 0 1 1 0 1 0 1 1 0 0 0 1 0 0 1 1 0 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 1 0 1 1 0 0 1 1 1 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 1 1 0 0 0 1 1 0 1 1 1 1 0 1 1 0 1 1 1 1 0 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 1 1 0 0 0 1 1 0 0 0 0 1 0 1 1 0 1 1 0 1 0 1 1 0 0 0 1 0 0 1 1 0 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 1 0 0 0 0 0 1 1 1 0 0 1 0 0 1 1 0 0 1 0 1 0 1 1 0 0 1 1 0 0 1 1 0 1 0 0 1 0 1 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 0 1 0 0 0 1 1 0 1 0 0 1 0 1 1 0 1 1 0 1 0 1 1 0 0 1 0 1 0 0 1 0 0 0 0 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 1 0 1 1 1 0 1 0 0 0 1 1 1 0 0 1 1 0 0 1 0 1 1 0 1 0 1 1 0 1 1 0 0 0 1 1 0 0 1 0 1 0 1 1 0 0 1 1 0 0 1 1 1 0 1 0 0 0 0 1 0 1 1 0 1 0 1 1 1 0 1 0 0 0 1 1 0 1 1 1 1 0 0 1 0 1 1 0 1 0 1 1 0 0 0 0 1 0 1 1 0 0 1 0 0 0 1 1 0 0 1 0 0 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 1 0 0 1 0 1 1 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 1 1 1 0 1 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 1 0 1 1 1 0 1 0 0 0 1 1 1 0 0 1 1 0 0 1 0 1 1 0 1 0 1 1 0 1 1 0 0 0 1 1 0 0 1 0 1 0 1 1 0 0 1 1 0 0 1 1 1 0 1 0 0 0 0 1 0 1 1 0 1 0 1 1 1 0 1 0 0 0 1 1 0 1 1 1 1 0 0 1 0 1 1 0 1 0 1 1 0 0 0 0 1 0 1 1 0 0 1 0 0 0 1 1 0 0 1 0 0 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 1 0 1 0 0 0 1 1 1 0 0 1 0 0 1 1 1 1 0 0 1 0 0 1 0 0 0 0 0 0 1 1 1 0 1 0 0 0 1 1 0 1 0 0 1 0 1 1 0 1 1 0 1 0 1 1 0 0 1 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 1 0 1 0 1 1 1 0 1 1 0 0 1 1 0 0 0 0 1 0 1 1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 1 0 0 1 0 0 1 1 0 0 1 0 1 0 1 1 0 0 0 0 1 0 1 1 0 0 1 0 0 0 0 1 0 1 1 0 1 0 1 1 0 0 1 0 1 0 1 1 1 1 0 0 0 0 1 1 1 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 1 1 1 0 0 0 0 0 1 1 1 0 0 1 0 0 1 1 0 0 1 0 1 0 1 1 0 0 1 1 0 0 1 1 0 1 0 0 1 0 1 1 1 1 0 0 0 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 0 0 1 0 1 1 1 0 0 0 0 0 1 1 1 0 0 0 0 0 1 1 0 0 1 0 1 0 1 1 0 1 1 1 0 0 1 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 1 0 1 1 0 0 1 1 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 0 0 1 0 1 1 1 0 0 0 0 0 1 1 1 0 0 0 0 0 1 1 0 0 1 0 1 0 1 1 0 1 1 1 0 0 1 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 1 1 0 0 0 0 0 1 1 1 0 0 1 0 0 1 1 0 0 1 0 1 0 1 1 0 0 1 1 0 0 1 1 0 1 0 0 1 0 1 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 1 1 1 0 1 0 0 0 1 1 0 1 0 0 1 0 1 1 0 1 1 0 1 0 1 1 0 0 1 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 1 1 0 1 0 0 1 0 0 0 0 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 1 0 1 1 1 0 1 0 0 0 1 1 1 0 0 1 1 0 0 1 0 1 1 0 1 0 1 1 0 1 1 0 0 0 1 1 0 0 1 0 1 0 1 1 0 0 1 1 0 0 1 1 1 0 1 0 0 0 0 1 0 1 1 0 1 0 1 1 1 0 1 0 0 0 1 1 0 1 1 1 1 0 0 1 0 1 1 0 1 0 1 1 0 0 0 0 1 0 1 1 0 0 1 0 0 0 1 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 1 0 1 1 0 0 1 1 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 0 0 1 0 1 1 1 0 0 0 0 0 1 1 1 0 0 0 0 0 1 1 0 0 1 0 1 0 1 1 0 1 1 1 0 0 1 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 1 1 0 0 0 0 0 1 1 1 0 0 1 0 0 1 1 0 0 1 0 1 0 1 1 0 0 1 1 0 0 1 1 0 1 0 0 1 0 1 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 1 0 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 1 1 1 0 1 0 0 0 1 1 0 1 0 0 1 0 1 1 0 1 1 0 1 0 1 1 0 0 1 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 1 1 0 1 0 0 1 0 0 0 0 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 1 0 1 1 1 0 1 0 0 0 1 1 1 0 0 1 1 0 0 1 0 1 1 0 1 0 1 1 0 1 1 0 0 0 1 1 0 0 1 0 1 0 1 1 0 0 1 1 0 0 1 1 1 0 1 0 0 0 0 1 0 1 1 0 1 0 1 1 1 0 1 0 0 0 1 1 0 1 1 1 1 0 0 1 0 1 1 0 1 0 1 1 0 0 0 0 1 0 1 1 0 0 1 0 0 0 1 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 1 1 0 0 0 1 1 0 0 0 0 1 0 1 1 0 1 1 0 1 0 1 1 0 0 0 1 0 0 1 1 0 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 1 1 0 0 0 1 1 0 0 0 0 1 0 1 1 0 1 1 0 1 0 1 1 0 0 0 1 0 0 1 1 0 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 1 1 0 0 0 1 1 0 0 0 0 1 0 1 1 0 1 1 0 1 0 1 1 0 0 0 1 0 0 1 1 0 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 0 1 0 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 1 1 0 0 0 1 1 0 0 0 0 1 0 1 1 0 1 1 0 1 0 1 1 0 0 0 1 0 0 1 1 0 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 0 1 1 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 1 1 0 0 0 1 1 0 0 0 0 1 0 1 1 0 1 1 0 1 0 1 1 0 0 0 1 0 0 1 1 0 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 1 0 0 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 1 0 1 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 1 0 1 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 1 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 0 1 1 0 1 1 0 0 0 0 1 0 1 1 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 0 1 1 0 1 1 0 0 1 0 0 0 1 1 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 0 1 1 0 1 1 0 0 1 0 0 0 1 1 1 0 0 1 0 0 0 1 0 0 0 0 0 0 1 1 1 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 0 1 1 0 1 1 0 0 0 0 1 0 1 1 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 1 0 0 0 1 1 0 0 1 0 1 0 1 1 0 0 0 1 0 0 1 1 1 0 1 0 1 0 1 1 0 0 1 1 1 0 0 1 0 0 0 0 0 0 1 1 1 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 0 1 1 0 1 1 0 0 0 0 1 0 1 1 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 0 1 1 0 1 1 0 0 1 0 0 0 1 1 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 0 1 1 0 1 1 0 0 1 0 0 0 1 1 1 0 0 1 0 0 0 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 0 1 1 0 1 1 0 0 0 0 1 0 1 1 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 1 0 0 0 1 1 0 0 1 0 1 0 1 1 0 0 0 1 0 0 1 1 1 0 1 0 1 0 1 1 0 0 1 1 1 0 0 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 1 1 0 0 0 1 1 0 0 0 0 1 0 1 1 0 1 1 0 1 0 1 1 0 0 0 1 0 0 1 1 0 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 1 0 1 1 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 1 1 0 0 0 1 1 0 0 0 0 1 0 1 1 0 1 1 0 1 0 1 1 0 0 0 1 0 0 1 1 0 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 1 1 0 0 0 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 1 0 0 1 0 1 1 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 1 0 0 0 1 1 0 0 1 0 1 0 1 1 0 0 0 1 0 0 1 1 1 0 1 0 1 0 1 1 0 0 1 1 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 1 0 1 1 1 0 0 1 0 0 1 1 0 0 0 0 1 0 1 1 1 0 1 0 0 0 0 1 0 0 0 0 0 0 1 1 1 0 1 1 1 0 0 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 1 0 1 1 0 0 1 1 1 0 0 1 0 0 0 0 0 0 1 1 0 1 1 1 0 0 1 1 0 1 0 0 1 0 1 1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 1 1 0 1 0 1 1 0 0 1 0 0 0 0 0 0 1 1 0 1 1 1 0 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 1 1 0 0 0 1 1 0 1 1 1 1 0 1 1 0 1 1 1 1 0 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 1 0 1 1 0 0 1 0 0 0 0 0 0 1 1 0 1 0 1 1 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 1 0 0 0 1 1 0 0 1 0 1 0 1 1 0 0 0 1 0 0 1 1 1 0 1 0 1 0 1 1 0 0 1 1 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 1 1 1 1 0 1 1 0 1 1 0 1 0 1 1 0 0 1 0 1 0 1 1 0 0 1 1 1 0 1 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 1 0 0 0 1 1 0 0 1 0 1 0 1 1 0 0 0 1 0 0 1 1 1 0 1 0 1 0 1 1 0 0 1 1 1 0 0 1 0 0 0 0 0 0 1 1 0 1 0 1 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 1 0 0 0 1 1 0 0 1 0 1 0 1 1 0 0 0 1 0 0 1 1 1 0 1 0 1 0 1 1 0 0 1 1 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 0 1 1 0 1 1 0 1 1 1 1 0 1 1 0 1 1 1 0 0 1 1 1 0 0 1 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 0 1 0 0 1 1 0 0 0 0 1 0 1 1 1 0 0 1 1 0 1 1 0 0 1 0 1 0 0 1 1 0 0 1 0 0 0 1 0 1 1 0 1 0 1 1 1 0 1 0 0 0 1 1 0 1 1 1 1 0 0 1 0 1 1 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 0 1 1 1 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 0 1 1 0 1 1 0 1 1 1 1 0 1 1 0 1 1 1 0 0 1 1 1 0 0 1 1 0 0 1 0 0 0 0 0 0 0 1 0 1 1 1 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 0 1 1 0 1 1 0 1 1 1 1 0 1 1 0 1 1 1 0 0 1 1 1 0 0 1 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 1 0 0 0 0 0 0 1 1 0 1 1 1 0 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 1 1 0 1 1 1 0 0 1 1 0 1 0 0 1 0 1 1 0 1 1 0 0 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 1 1 0 0 0 1 1 0 0 1 0 1 0 1 1 0 1 1 1 0 0 1 1 0 0 1 1 1 0 1 1 1 0 1 0 0 0 1 1 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 0 1 1 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 1 0 0 0 1 1 0 0 1 0 1 0 1 1 0 0 0 1 0 0 1 1 1 0 1 0 1 0 1 1 0 0 1 1 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 1 0 1 0 1 1 1 0 1 1 0 0 1 1 0 0 0 0 1 0 1 1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 1 0 0 0 1 1 0 0 1 0 1 0 1 1 0 0 0 1 0 0 1 1 1 0 1 0 1 0 1 1 0 0 1 1 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 1 0 0 1 0 0 1 1 0 0 1 0 1 0 1 1 0 0 0 0 1 0 1 1 0 0 1 0 0 0 0 1 0 1 1 0 1 0 1 1 0 0 1 0 1 0 1 1 1 1 0 0 0 0 1 1 1 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 1 1 0 0 0 1 1 0 0 0 0 1 0 1 1 0 1 1 0 1 0 1 1 0 0 0 1 0 0 1 1 0 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 1 0 1 1 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 0 1 1 0 1 1 0 1 1 1 1 0 1 1 0 1 1 1 0 0 1 1 1 0 0 1 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 0 1 1 0 1 1 0 1 1 1 1 0 1 1 1 0 1 0 1 0 1 1 0 1 1 1 0 0 1 1 1 0 1 0 0 0 0 1 0 1 1 0 1 0 1 1 0 1 0 0 0 0 1 1 0 0 0 0 1 0 1 1 0 1 1 0 0 0 1 1 1 0 1 0 0 0 0 1 0 0 0 0 0 0 1 1 0 1 1 1 0 0 1 1 0 1 0 0 1 0 1 1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 1 1 0 1 0 1 1 0 0 1 0 0 0 0 0 0 1 1 0 1 0 1 1 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 0 1 1 0 1 1 0 1 1 1 1 0 1 1 0 1 1 1 0 0 1 1 1 0 0 1 1 0 0 1 0 0 0 0 0 0 0 1 0 1 1 1 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 0 1 1 0 1 1 0 1 1 1 1 0 1 1 0 1 1 1 0 0 1 1 1 0 0 1 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 1 0 0 0 0 0 0 1 1 0 1 0 1 1 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 1 1 0 1 1 1 0 0 1 1 0 1 0 0 1 0 1 1 0 1 1 0 0 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 1 1 0 0 0 1 1 0 0 0 0 1 0 1 1 0 1 1 0 1 0 1 1 0 0 0 1 0 0 1 1 0 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 1 0 0 0 0 0 1 1 1 0 0 1 0 0 1 1 0 0 1 0 1 0 1 1 0 0 1 1 0 0 1 1 0 1 0 0 1 0 1 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 0 1 0 0 0 1 1 0 1 0 0 1 0 1 1 0 1 1 0 1 0 1 1 0 0 1 0 1 0 0 1 0 0 0 0 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 1 0 1 1 1 0 1 0 0 0 1 1 1 0 0 1 1 0 0 1 0 1 1 0 1 0 1 1 0 1 1 0 0 0 1 1 0 0 1 0 1 0 1 1 0 0 1 1 0 0 1 1 1 0 1 0 0 0 0 1 0 1 1 0 1 0 1 1 1 0 1 0 0 0 1 1 0 1 1 1 1 0 0 1 0 1 1 0 1 0 1 1 0 0 1 0 1 0 1 1 1 1 0 0 0 0 1 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 1 1 0 1 1 1 0 0 1 1 0 0 1 0 0 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 1 0 0 1 0 1 1 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 1 1 1 0 1 0 0 1 0 0 0 0 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 1 0 1 1 1 0 1 0 0 0 1 1 1 0 0 1 1 0 0 1 0 1 1 0 1 0 1 1 0 1 1 0 0 0 1 1 0 0 1 0 1 0 1 1 0 0 1 1 0 0 1 1 1 0 1 0 0 0 0 1 0 1 1 0 1 0 1 1 1 0 1 0 0 0 1 1 0 1 1 1 1 0 0 1 0 1 1 0 1 0 1 1 0 0 1 0 1 0 1 1 1 1 0 0 0 0 1 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 1 1 0 1 1 1 0 0 1 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 1 0 0 1 0 1 1 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 1 1 1 0 1 0 0 1 0 0 0 0 0 0 1 1 1 0 0 1 1 0 1 1 1 0 1 0 1 0 1 1 0 0 0 1 1 0 1 1 0 0 0 1 1 0 1 1 0 0 1 0 1 0 1 1 1 0 0 1 1 0 1 1 1 0 0 1 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 0 1 1 0 1 1 0 0 0 0 1 0 1 1 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 1 0 1 0 0 0 1 1 1 0 0 1 0 0 1 1 1 1 0 0 1 0 0 1 0 0 0 0 0 0 1 1 1 0 1 0 0 0 1 1 0 1 0 0 1 0 1 1 0 1 1 0 1 0 1 1 0 0 1 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 1 0 1 0 1 1 1 0 1 1 0 0 1 1 0 0 0 0 1 0 1 1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 1 0 0 1 0 0 1 1 0 0 1 0 1 0 1 1 0 0 0 0 1 0 1 1 0 0 1 0 0 0 0 1 0 1 1 0 1 0 1 1 0 0 1 0 1 0 1 1 1 1 0 0 0 0 1 1 1 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 1 1 1 0 0 0 0 0 1 1 1 0 0 1 0 0 1 1 0 0 1 0 1 0 1 1 0 0 1 1 0 0 1 1 0 1 0 0 1 0 1 1 1 1 0 0 0 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 1 0 1 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 0 1 1 0 1 1 0 1 1 1 1 0 1 1 1 0 1 0 1 0 1 1 0 1 1 1 0 0 1 1 1 0 1 0 0 0 0 1 0 1 1 0 1 0 1 1 0 1 0 0 0 0 1 1 0 0 0 0 1 0 1 1 0 1 1 0 0 0 1 1 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 0 0 1 0 1 1 1 0 0 0 0 0 1 1 1 0 0 0 0 0 1 1 0 0 1 0 1 0 1 1 0 1 1 1 0 0 1 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 1 1 0 0 0 0 0 1 1 1 0 0 1 0 0 1 1 0 0 1 0 1 0 1 1 0 0 1 1 0 0 1 1 0 1 0 0 1 0 1 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 1 1 1 0 1 0 0 0 1 1 0 1 0 0 1 0 1 1 0 1 1 0 1 0 1 1 0 0 1 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 1 1 0 1 0 0 1 0 0 0 0 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 1 0 1 1 1 0 1 0 0 0 1 1 1 0 0 1 1 0 0 1 0 1 1 0 1 0 1 1 0 1 1 0 0 0 1 1 0 0 1 0 1 0 1 1 0 0 1 1 0 0 1 1 1 0 1 0 0 0 0 1 0 1 1 0 1 0 1 1 1 0 1 0 0 0 1 1 0 1 1 1 1 0 0 1 0 1 1 0 1 0 1 1 0 0 1 0 1 0 1 1 1 1 0 0 0 0 1 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 1 1 0 1 1 1 0 0 1 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 0 1 1 0 1 1 0 1 1 1 1 0 1 1 1 0 1 0 1 0 1 1 0 1 1 1 0 0 1 1 1 0 1 0 0 0 0 1 0 1 1 0 1 0 1 1 0 1 0 0 0 0 1 1 0 0 0 0 1 0 1 1 0 1 1 0 0 0 1 1 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 0 0 1 0 1 1 1 0 0 0 0 0 1 1 1 0 0 0 0 0 1 1 0 0 1 0 1 0 1 1 0 1 1 1 0 0 1 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 1 1 0 0 0 0 0 1 1 1 0 0 1 0 0 1 1 0 0 1 0 1 0 1 1 0 0 1 1 0 0 1 1 0 1 0 0 1 0 1 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 1 0 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 1 1 1 0 1 0 0 0 1 1 0 1 0 0 1 0 1 1 0 1 1 0 1 0 1 1 0 0 1 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 1 1 0 1 0 0 1 0 0 0 0 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 1 0 1 1 1 0 1 0 0 0 1 1 1 0 0 1 1 0 0 1 0 1 1 0 1 0 1 1 0 1 1 0 0 0 1 1 0 0 1 0 1 0 1 1 0 0 1 1 0 0 1 1 1 0 1 0 0 0 0 1 0 1 1 0 1 0 1 1 1 0 1 0 0 0 1 1 0 1 1 1 1 0 0 1 0 1 1 0 1 0 1 1 0 0 1 0 1 0 1 1 1 1 0 0 0 0 1 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 1 1 0 1 1 1 0 0 1 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 0 0 1 0 1 0 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 0 0 1 0 1 0) debug (' (0 0 0 0 0 0 0 1)) debug (0 0 0 0 0 0 0 1) debug (1 / 256) debug 0 debug (0 / 1) debug (1 / 256) debug (0 / 1) debug false debug 1 debug (0 / 2) debug (1 / 256) debug (0 / 2) debug false debug 2 debug (0 / 4) debug (1 / 256) debug (0 / 4) debug false debug 3 debug (0 / 8) debug (1 / 256) debug (0 / 8) debug false debug 4 debug (0 / 16) debug (1 / 256) debug (0 / 16) debug false debug 5 debug (0 / 32) debug (1 / 256) debug (0 / 32) debug false debug 6 debug (0 / 64) debug (1 / 256) debug (0 / 64) debug false debug 7 debug (0 / 128) debug (1 / 256) debug (0 / 128) debug false debug 8 debug (1 / 256) debug (1 / 256) debug (1 / 256) debug true value (failure out-of-data () failure out-of-data () fai lure out-of-data () failure out-of-data () failure out-of-data () failure out-of-data () failure out -of-data () failure out-of-data () failure out-of- data () failure out-of-data () success () () failu re out-of-data () failure out-of-data () failure o ut-of-data () failure out-of-data () failure out-o f-data () failure out-of-data () failure out-of-da ta () failure out-of-data () failure out-of-data ( ) failure out-of-data () failure out-of-data () fa ilure out-of-data () failure out-of-data () failur e out-of-data () failure out-of-data () failure ou t-of-data () failure out-of-data () failure out-of -data () failure out-of-data () failure out-of-dat a () failure out-of-data () failure out-of-data () failure out-of-data () failure out-of-data () fai lure out-of-data () failure out-of-data () failure out-of-data () failure out-of-data () failure out -of-data () failure out-of-data () failure out-of- data () failure out-of-data () failure out-of-data () failure out-of-data () failure out-of-data () failure out-of-data () failure out-of-data () fail ure out-of-data () failure out-of-data () failure out-of-data () failure out-of-data () failure out- of-data () failure out-of-data () failure out-of-d ata () failure out-of-data () failure out-of-data () failure out-of-data () failure out-of-data () f ailure out-of-data () failure out-of-data () failu re out-of-data () failure out-of-data () failure o ut-of-data () failure out-of-data () failure out-o f-data () failure out-of-data () failure out-of-da ta () failure out-of-data () failure out-of-data ( ) failure out-of-data () failure out-of-data () fa ilure out-of-data () failure out-of-data () failur e out-of-data () failure out-of-data () failure ou t-of-data () failure out-of-data () failure out-of -data () failure out-of-data () failure out-of-dat a () failure out-of-data () failure out-of-data () failure out-of-data () failure out-of-data () fai lure out-of-data () failure out-of-data () failure out-of-data () failure out-of-data () failure out -of-data () failure out-of-data () failure out-of- data () failure out-of-data () failure out-of-data () failure out-of-data () failure out-of-data () failure out-of-data () failure out-of-data () fail ure out-of-data () failure out-of-data () failure out-of-data () failure out-of-data () failure out- of-data () failure out-of-data () failure out-of-d ata () failure out-of-data () failure out-of-data () failure out-of-data () failure out-of-data () f ailure out-of-data () failure out-of-data () failu re out-of-data () failure out-of-data () failure o ut-of-data () failure out-of-data () failure out-o f-data () failure out-of-data () failure out-of-da ta () failure out-of-data () failure out-of-data ( ) failure out-of-data () failure out-of-data () fa ilure out-of-data () failure out-of-data () failur e out-of-data () failure out-of-data () failure ou t-of-data () failure out-of-data () failure out-of -data () failure out-of-data () failure out-of-dat a () failure out-of-data () failure out-of-data () failure out-of-data () failure out-of-data () fai lure out-of-data () failure out-of-data () failure out-of-data () failure out-of-data () failure out -of-data () failure out-of-data () failure out-of- data () failure out-of-data () failure out-of-data () failure out-of-data () failure out-of-data () failure out-of-data () failure out-of-data () fail ure out-of-data () failure out-of-data () failure out-of-data () failure out-of-data () failure out- of-data () failure out-of-data () failure out-of-d ata () failure out-of-data () failure out-of-data () failure out-of-data () failure out-of-data () f ailure out-of-data () failure out-of-data () failu re out-of-data () failure out-of-data () failure o ut-of-data () failure out-of-data () failure out-o f-data () failure out-of-data () failure out-of-da ta () failure out-of-data () failure out-of-data ( ) failure out-of-data () failure out-of-data () fa ilure out-of-data () failure out-of-data () failur e out-of-data () failure out-of-data () failure ou t-of-data () failure out-of-data () failure out-of -data () failure out-of-data () failure out-of-dat a () failure out-of-data () failure out-of-data () failure out-of-data () failure out-of-data () fai lure out-of-data () failure out-of-data () failure out-of-data () failure out-of-data () failure out -of-data () failure out-of-data () failure out-of- data () failure out-of-data () failure out-of-data () failure out-of-data () failure out-of-data () failure out-of-data () failure out-of-data () fail ure out-of-data () failure out-of-data () failure out-of-data () failure out-of-data () failure out- of-data () failure out-of-data () failure out-of-d ata () failure out-of-data () failure out-of-data () failure out-of-data () failure out-of-data () f ailure out-of-data () failure out-of-data () failu re out-of-data () failure out-of-data () failure o ut-of-data () failure out-of-data () failure out-o f-data () failure out-of-data () failure out-of-da ta () failure out-of-data () failure out-of-data ( ) failure out-of-data () failure out-of-data () fa ilure out-of-data () failure out-of-data () failur e out-of-data () failure out-of-data () failure ou t-of-data () failure out-of-data () failure out-of -data () failure out-of-data () failure out-of-dat a () failure out-of-data () failure out-of-data () failure out-of-data () failure out-of-data () fai lure out-of-data () failure out-of-data () failure out-of-data () failure out-of-data () failure out -of-data () failure out-of-data () failure out-of- data () failure out-of-data () failure out-of-data () failure out-of-data () failure out-of-data () failure out-of-data () failure out-of-data () fail ure out-of-data () failure out-of-data () failure out-of-data () failure out-of-data () failure out- of-data () failure out-of-data () failure out-of-d ata () failure out-of-data ()) End of LISP Run Elapsed time is 2 seconds.