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>
#include<cstdio>
#include<iostream>
#include<map>
#include<string>
#include<queue>
#include<map>
#include<vector>
#include<set>
#include<cstring>
using namespace std;
typedef long long ll;
ll a[1000005];
char s[1000005];
ll b[1000005];
int main()
{
	ll n;
	scanf("%lld",&n);
	scanf(" %s",s);
	bool one=0;
	for(ll i=0;i<n;i++)
	{
		a[i]=s[i]-'1';
		if(a[i]==1) one=true;
	}
	if(!one)
	{
		for(ll i=0;i<n;i++) a[i]/=2;
	}
	else
	{
		for(ll i=0;i<n;i++) a[i]%=2;
	}
	ll ans=0;
	for(ll i=0;i<n;i++)
	{
		ll j=n-1-i;
		if((j^i)==(j+i))
		{
			ans^=a[i];
		}
	}
	if(!one)
	{
		ans*=2;
	}
	printf("%lld",ans);
}