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: Runtime Error)

(defun main ()
  (let* ((n (read))
         (vec (make-array n :initial-element 0)))
    (dotimes (i n)
      (setf (svref vec i)
            (- (char-code (read-char)) 48)))
    (princ (f n vec))))

(defun f (n vec)
  (let ((cache (make-hash-table :test #'equal)))
    (labels ((x (i j)
               (declare (optimize (speed 3))
                        (type fixnum i j))
               (or (identity (gethash (cons i j) cache))
                   (setf (gethash (cons i j) cache)
                         (if (<= i 0)
                             (svref vec j)
                             (abs (the fixnum (- (the fixnum (x (1- i) j))
                                                 (the fixnum (x (1- i) (1+ j)))))))))))
      (x (1- n) 0))))

(main)