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 = 1000005;

int n;
char a[MAXN];

int main(){
	scanf("%d %s", &n, a);
	
	int num1 = 0, num2 = 0;
	bool foundone = false;
	
	for(int i = 0; i < n; i++){
		a[i]--;
		int c = ((n - 1) & i) == i;
		
		if(a[i] == '0'){
			continue;
		}else if(a[i] == '1'){
			foundone = true;
			num1 ^= c;
		}else{
			num2 ^= c;
		}
	}
	
	if(foundone){
		printf("%d\n", num1);
	}else{
		printf("%d\n", 2 * num2);
	}
	
	
	return 0;
}