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>
#define SIZE 1000005
using namespace std;

int A[SIZE];
char str[SIZE];

int main()
{
	int n;
	scanf("%d",&n);
	scanf("%s",&str);
	bool up=true;
	for(int i=0;i<n;i++)
	{
		A[i]=str[i]-'0';
		A[i]--;
		if(A[i]==1) up=false;
	}
	if(up)
	{
		for(int i=0;i<n;i++) A[i]/=2;
	}
	int ret=0;
	for(int i=0;i<n;i++)
	{
		if(((n-1)&i)==i)
		{
			ret^=A[i]%2;
		}
	}
	if(up) ret*=2;
	printf("%d\n",ret);
	return 0;
}