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>
#define maxn 2000010
using namespace std;
int n,w,st=0;
int ans[2][10]={{0,1,0,1,1,2,1,0},{0,1,0,1,1,0,1,0}};
bool flag=0; 
char s[maxn];
int main(){
	scanf("%d%s",&n,s);
	n--;
	for(register int i=0;i<=n;i++){
		if(s[i]=='2')flag=1;
		w=s[i]-'1';
		st^=(1<<w)&((n==(n|i))?7:0);
	}
	printf("%d",ans[flag][st]);
	return 0;
}