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 ll long long
using namespace std;
int n,i,flag,a[1000010],b[1000010];
char s[1000010];
int main(){
	scanf("%d",&n);
	scanf("%s",s);
	for(i=0;i<n;i++){
		a[i]=s[i]-'1';
		if(a[i]==1)flag=1;
		b[a[i]]+=(((n-1)&i)==i);
	}
	if(b[1]&1)puts("1"); 
	 else if(!flag&&b[2]&1)puts("2");
	  else puts("0");
}