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=1e6+50,mod=2;
int n,cc[N];char a[N];bool fl;
int C(int n,int m){return m>n?0:n<2?1:C(n&1,m&1)*C(n>>1,m>>1);}
int main(){
	scanf("%d%s",&n,a+1);
	for(int i=1;i<=n;i++)if(a[i]=='2')fl=1;
	if(fl){
		int ans=0;
		// if(!(n&1)&&n!=2)ans+=a[2]+a[n-1];
		for(int i=1;i<=n;i++)if(a[i]=='2')ans+=C(n-1,i-1);
		putchar(ans&1?'1':'0');
	}
	else{
		int ans=0;
		for(int i=1;i<=n;i++)if(a[i]=='3')ans+=C(n-1,i-1);
		putchar(ans&1?'2':'0');
	}
	return 0;
}