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;
int n,a[1000005],p,vis[3];
char s[1000005];

int main(){
	scanf("%d",&n);
	scanf("%s",s+1);
	for(int i=1;i<n;i++) a[i]=abs(s[i]-s[i+1]),vis[a[i]]=1;
	if(!vis[1]) for(int i=1;i<n;i++) a[i]/=2;
	else for(int i=1;i<n;i++) a[i]%=2;
	int S=n-2;
	for(int i=0;i<n-1;i++) if((S&i)==i) p+=a[i+1];
	int op=p%2;
	if(!vis[1]) if(op) op=2;
	printf("%d\n",op);

	return 0;
}