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 = 1e6 + 10;

int n , cnt[3] , d[3];
char a[N];

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