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;
const int N=1000005;
char s[N];
int a[N],b[N],n;
int sol()
{
	int r=0;
	for(int i=0;i<n;i++)
		r=r^((((n-1)&i)==i)&a[i]);
	return r;
}
int main()
{
	scanf("%d%s",&n,s);
	for(int i=0;i<n;i++)
		b[i]=s[i]-'1';
	int fl=0;
	for(int i=0;i<n;i++)
		if(b[i]==1)
			fl=1;
	for(int i=0;i<n;i++)
		a[i]=b[i]&1;
	if(sol())
		puts("1");
	else
	{
		if(fl)
			puts("0");
		else
		{
			for(int i=0;i<n;i++)
				a[i]=b[i]/2;
			if(sol())
				puts("2");
			else
				puts("0");
		}
	}
	return 0;
}