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 N=1000005,E=262144;
const int M=998244353;
int n,m,i,j,s,a[N];
char c[N];
bool flag;
int main()
{
	scanf("%d",&n);
	scanf("%s",c);
	--n;
	for(i=0;i<n;++i)
	{
		a[i]=abs(c[i]-c[i+1]);
		if(a[i]==1)
			flag=true;
	}
	if(flag)
	{
		for(i=0;i<n;++i)
		{
			a[i]&=1;
			if(((n-1)&i)==i)
				s^=a[i];
		}
		cout<<s;
	}
	else
	{
		for(i=0;i<n;++i)
			if(((n-1)&i)==i)
				s^=a[i];
		cout<<s;
	}
}