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 N = 1000005;
int n, a[N];
char s[N];
bool ans;

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