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<iostream>
#include<cstdio>
using namespace std;
const int N=1000005;
int n;
char s[N];
int a[N];
int cnt[3];
int main()
{
	scanf("%d",&n);
	scanf("%s",s+1);
	for(int i=1;i<=n;i++)
		a[i]=s[i]-'1';
	bool flag=false;
	for(int i=1;i<=n;i++)
	{
		if(a[i]==1) flag=true;
		cnt[a[i]]+=(((n-1)&(i-1))==(i-1));
	}
	if(cnt[1]&1) printf("1");
	else if(!flag&&(cnt[2]&1)) printf("2");
	else printf("0");
	return 0;
}