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 maxn=1000005;
int n,ans;
char s[maxn];
int a[maxn];

int main(){
	scanf("%d%s",&n,s);
	for(int i=0;i<n-1;i++){
		a[i]=abs(s[i]-s[i+1]);
		if(((n-2)&i)==i)ans^=(a[i]&1);
	}
	if(ans){
		puts("1");
		return 0;
	}
	ans=0;
	for(int i=0;i<n-1;i++){
		if(a[i]==1){
			puts("0");
			return 0;
		}
		if(((n-2)&i)==i)ans^=(a[i]==2);
	}
	if(ans)puts("2");
	else puts("0");
	return 0;
}