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;
int n, a[1000005];
char str[1000005];
int main() {
	scanf("%d %s", &n, str);
	for (int i = 0; i < n; i++) a[i] = str[i] - '1';
	int flag1 = 0;
	for (int i = 0; i < n; i++) if (a[i] == 2) a[i] = 0; else if (a[i] == 1) flag1 = 1;
	int ans = 0;
	for (int i = 0; i < n; i++) if (((n - 1) & i) == i) ans ^= a[i];
	if (!ans && !flag1) {
		for (int i = 0; i < n; i++) a[i] = (str[i] - '1') / 2;
		for (int i = 0; i < n; i++) if (((n - 1) & i) == i) ans ^= a[i];
		ans *= 2;
	}
	printf("%d\n", ans);
	return 0;
}