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;
#define N 1000005
int n,t1,t2,cnt[N];bool fl;char a[N];
int main()
{
	scanf("%d %s",&n,a);
	if(n==2) {printf("%d\n",abs(a[0]-a[1]));return 0;}
	for(int i=1;i<=n;++i) if(!(i%2)) cnt[i]=cnt[i/2]+1;
	for(int i=1;i<=n;++i) cnt[i]+=cnt[i-1];
	for(int i=0,x,t;i<n-1;++i)
	{
		x=abs(a[i]-a[i+1]);
		if(cnt[i]<cnt[n-2]-cnt[n-2-i]) t=0;else t=1;
		if(x==1) t1=(t1+t)%2,fl=1;if(x==2) t2=(t2+t)%2; 
	}if(t1) puts("1");else if(fl || (!fl && !t2)) puts("0");else puts("2");
	return 0;
}