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; 
char s[1010101];
int main()
{
	int N;
	scanf("%d", &N);
	scanf("%s", s);
	
	bool flag = 0;
	int ans = 0;
	for(int i = 0; i < N; i++)
	{
		if(s[i] == '2')
			flag = 1;
		if(((N-1)&i) == i)
			ans ^= s[i] - '1';
	}
	if(flag)
		printf("%d\n", ans & 1);
	else
		printf("%d\n", ans & 2);
		
	return 0;
}