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:
#import<bits/stdc++.h>
#define endl '\n'
using namespace std;
int i,j,k,m,n,p=1,x,y,z,a[1000005],b[1000005],c[1000005];
string s;
int main()
{
	ios_base::sync_with_stdio(0);
	cin.tie(0);
	cout.tie(0);
	cin>>n>>s;
	for(;i<n;i++)z+=s[i]&1;
	if(z==n)
	{
		p=2;
		for(;i--;)a[i]=(s[i]&2)>>1;
	}
	else
	{
		for(;i--;)a[i]=!(s[i]&1);
	}
	for(i=0;++i<n;)
	{
		if(i&1)
		{
			c[i]=c[i-1];
		}
		else
		{
			b[i]=b[i>>1]+1;
			c[i]=c[i-1]+b[i];
		}
		//cout<<b[i]<<' '<<c[i]<<endl;
	}
	k=n-1;
	//for(i=0;i<n;i++)cout<<a[i];cout<<endl;
	for(i=0;i<n;i++)
	{
		if(a[i])
		{
			if(c[k]-c[i]==c[k-i])m=!m;
		}
		//cout<<i<<' '<<c[k]<<' '<<c[i]<<' '<<c[k-i]<<' '<<m<<endl;
	}
	cout<<m*p;
}