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>
#include <cstdlib>
#include <cstring>
using namespace std;
const int maxn=1e6+10;
int n,a[maxn],sum[maxn],v[maxn],k=2,ans;
char s[maxn];
int main()
{
	scanf("%d%s",&n,s+1);
	for (int i=1;i<=n;i++)
	{
		a[i]=s[i]-'1';
		if (a[i]==1) k=1;
	}
	for (int i=1;i<=n;i++)
	{
		v[i]=(i&1?0:v[i/2]+1);
		sum[i]=sum[i-1]+v[i];
	}
	for (int i=1;i<=n;i++)
	if (sum[n-1]==sum[i-1]+sum[n-i]) ans=(ans+a[i]/k)%2;
	printf("%d\n",ans*k);
return 0;
}