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<cstdio>

using namespace std;

char c[1000001];
int a[1000001];
int main(){
	int n;
	scanf("%d",&n);
	scanf("%s",c+1);
	int ans=0;
	for(int i=1;i<=n;i++){
		int w=1;
		for(int j=0;j<20;j++)
			if(!(n-1>>j&1)&&((i-1>>j)&1))w=0;
		int z=w?c[i]-'1':0;
		a[i]=z;
		ans^=z;
	}
	int ok=0;
	for(int i=1;i<=n;i++)
		if(c[i]=='2')ok=1;
	if(!ok){
		printf("%d\n",ans&2);
	}
	else printf("%d\n",ans&1);
}