Problem:
Score : 700 points

Problem Statement

Given is a sequence of N digits a_1a_2\ldots a_N, where each element is 1, 2, or 3.
Let x_{i,j} defined as follows:

x_{1,j} := a_j \quad (1 \leq j \leq N)

x_{i,j} := | x_{i-1,j} - x_{i-1,j+1} | \quad (2 \leq i \leq N and 1 \leq j \leq N+1-i)

Find x_{N,1}.

Constraints

2 \leq N \leq 10^6

a_i = 1,2,3 (1 \leq i \leq N)

Input

Input is given from Standard Input in the following format:

N
a_1a_2\ldotsa_N

Output

Print x_{N,1}.

Sample Input 1

4
1231

Sample Output 1

1

x_{1,1},x_{1,2},x_{1,3},x_{1,4} are respectively 1,2,3,1.

x_{2,1},x_{2,2},x_{2,3} are respectively |1-2| = 1,|2-3| = 1,|3-1| = 2.

x_{3,1},x_{3,2} are respectively |1-1| = 0,|1-2| = 1.

Finally, x_{4,1} = |0-1| = 1, so the answer is 1.

Sample Input 2

10
2311312312

Sample Output 2

0

Solution in Common Lisp (SBCL 1.1.14) (judge verdict: Time Limit Exceeded)

(defvar N (read))

(defun abskaisa (old &optional new)
  (if (null (cdr old))
      (nreverse new)
    (abskaisa (cdr old) (cons (abs (- (cadr old) (car old))) new))))

(defun solve-stupid ()
  (let ((a (mapcar #'digit-char-p (concatenate 'list (read-line)))))
    (dotimes (x (1- N))
      (setf a (abskaisa a))
      )
    (princ (car a))
    )
  )

(defun cunning-solve ()
  (let* ((str (read-line))
	 (hd (mapcar #'digit-char-p (concatenate 'list (subseq str 0 4))))
	 (tl (mapcar #'digit-char-p (concatenate 'list (subseq str (- N 4)))))
	 (hdb (abskaisa (abskaisa hd)))
	 )
    (princ (list hdb tl))))

(solve-stupid)