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<iostream>
#include<cstdio>
#define Abs(x) ((x)<0?-(x):(x))
#define FOR(i,a,b) for(int i=a;i<=b;i++)
using namespace std;
const int N=10001000;
int n,fl,ans,a[N];
char s[N];
int main(){
	//freopen("1.in","r",stdin);
	//freopen("1.out","w",stdout);
	scanf("%d%s",&n,s);
	n-=2;
	FOR(i,0,n) a[i]=Abs(s[i+1]-s[i]);//cerr<<a[i];
	fl=2;
	FOR(i,0,n)if(a[i]==1) fl=1;
	FOR(i,0,n)if(a[i]==fl) ans^=(n&i)==i;
	ans*=fl;
	cout<<ans<<'\n';
}