Problem: 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}.

Examples

Input

4
1231


Output

1


Input

10
2311312312


Output

0

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;

const int maxn = 1e6;
int n, a[maxn + 3];
char s[maxn + 3];

int main() {
	scanf("%d %s", &n, s), n--;
	bool flag = true;
	for (int i = 0; i <= n; i++) {
		a[i] = s[i] - '1';
		flag &= a[i] != 1;
	}
	if (flag) {
		bool ans = 0;
		for (int i = 0; i <= n; i++) {
			ans ^= (a[i] == 2) && ((i & n) == i);
		}
		puts(ans ? "2" : "0");
	} else {
		bool ans = 0;
		for (int i = 0; i <= n; i++) {
			ans ^= (a[i] & 1) && ((i & n) == i);
		}
		puts(ans ? "1" : "0");
	}
	return 0;
}