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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
 
using namespace std;
 
const int N = 1000010;
 
char s[N];
int n, a[N], b[N];
 
int main() {
  scanf("%d %s", &n, s + 1); --n;
  bool isOne = 0;
  for (int i = 1; i <= n; ++i) {
    a[i] = abs(s[i] - s[i + 1]);
    if (a[i] == 1) isOne = 1;
  }
  // cout << brute() << " ";
  int fac = 1;
  if (!isOne) {
    for (int i = 1; i <= n; ++i) a[i] >>= 1;
    fac = 2;
  } 
  int sum = 0;
  for (int i = 1; i <= n; ++i) {
  	if( ((n-1) | (i-1)) == (n-1) ) {
  		sum += (a[i] & 1), sum &= 1;
  	}
  }
  cout << sum * fac << '\n';
  return 0;
}