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 <algorithm>
#include <cstdio>
using namespace std;
const int N = 1e6 + 10;
int a[N], n;
char s[N];
int main() {
	scanf("%d%s", &n, s); n --;
	for(int i = 0; i <= n; i ++) {
		a[i] = s[i] - '0' - 1;
	}
	int ans = 0;
	for(int i = 0; i <= n; i ++) {
		if((n & i) == i) ans ^= a[i] & 1;
	}
	if(ans == 1) puts("1");
	else {
		for(int i = 0; i <= n; i ++) {
			if(a[i] == 1) { puts("0"); return 0; }
			a[i] >>= 1;
		}
		ans = 0;
		for(int i = 0; i <= n; i ++) {
			if((n & i) == i) ans ^= a[i] & 1;
		}
		printf("%d\n", ans ? 2 : 0);
	}
	return 0;
}