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;
int cnt[3];
int main(){
	int n;char ch;int f=0;
	cin>>n;
	for(int i=0;i<n;++i)
		cin>>ch,f=(ch=='2'?1:f),cnt[ch-'0'-1]+=(((n-1)&i)==i);
	if(cnt[1]&1) puts("1");
	else if(cnt[2]%2==1 && f==0) puts("2");
	else puts("0");
	return 0;
}