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 rep(i,n) for(int i=0;i<(n);i++)

using namespace std;

int parity(int n,int r){
	rep(i,20) if((n>>i&1)<(r>>i&1)) return 0;
	return 1;
}

int main(){
	int n;
	string s; cin>>n>>s;

	rep(i,n-1) s[i]=abs(s[i]-s[i+1])+'0';
	s.pop_back();
	n--;

	int res=0;
	rep(i,n){
		if(parity(n-1,i)==1) res=(res+s[i]-'0')%2;
	}
	if(res==1) return puts("1"),0;

	if(count(s.begin(),s.end(),'1')>0) return puts("0"),0;

	rep(i,n) if(s[i]=='2') s[i]='1';

	res=0;
	rep(i,n){
		if(parity(n-1,i)==1) res=(res+s[i]-'0')%2;
	}
	puts(res==0?"0":"2");

	return 0;
}