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>
#define Tp template<typename Ty>
#define Ts template<typename Ty,typename... Ar>
#define Reg register
#define RI Reg int
#define Con const
#define CI Con int&
#define I inline
#define W while
#define N 1000000
using namespace std;
int n,a[N+5];char s[N+5];
int main()
{
	RI i;for(scanf("%d%s",&n,s+1),--n,i=1;i<=n;++i) a[i]=abs(s[i]-s[i+1]);
	RI f=1;for(i=1;i<=n;++i) if(a[i]==1) {f=0;break;}
	for(i=1;i<=n;++i) a[i]==2&&(a[i]=f);
	RI ans=0;for(i=1;i<=n;++i) (((n-1)^(i-1))==n-i)&&(ans^=a[i]);
	return printf("%d",ans*(f+1)),0;
}