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 (Clang 3.8.0) (judge verdict: Runtime Error)

#include <stdio.h>
#include <stdlib.h>

int main(void) {
  int n;
  scanf("%d", &n);
  int **x = calloc(n + 1, sizeof(int*));
  for(int i = 0;i <= n;i++) {
    x[i] = calloc(n + 1, sizeof(int));
  }
  char *a = calloc(n + 1, sizeof(char));
  scanf("%s", a + 1);
  for(int i = 1;i <= n;i++) {
    x[1][i] = a[i] - '0';
  }
  for(int i = 2;i <= n;i++) {
    for(int j = 1;j <= n + 1 - i;j++) {
      x[i][j] = abs(x[i-1][j] - x[i-1][j+1]);
    }
  }
  printf("%d\n", x[n][1]);
  return 0;
}