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 C (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

#include <stdio.h>
int main()
{
  int N,i,k;
  scanf("%d\n",&N);
  char a[N + 1];
  i = 0;
  while (i < N)
  {
    scanf("%c",&a[i]);
    i++;
  }
  a[i] = '\0';
  i = 0;
  while (a[1] != '\0')
  {
    i = 0;
    while (a[i + 1])
    {
      //printf("%c %c\n",a[i],a[i + 1]);
      a[i] = (a[i] - a[i + 1]);
      if (a[i] < 0)
        a[i] = '0' - a[i];
      else
        a[i] += '0';
      //printf("%c\n",a[i]);
      i++;
    }
    a[i] = '\0';
    k = 0;
    while (a[k])
      k++;
    //printf("%d\n",k);
  }
  printf("%c",a[0]);
}