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 main()
{
	int n;
	string s;
	cin >> n >> s;
	vector<int> v;
	for (char c:s)
	v.push_back(c-'0');
	for (int i=0;i<n-1;i++)
	v[i]=abs(v[i]-v[i+1]);
	v.pop_back();
	n--;
	if (count(v.begin(),v.end(),1))
	{
		for (int &i:v)
		i%=2;
	}
	for (int i=0;i<20;i++)
	{
		if ((n-1)&(1<<i))
		{
			vector<int> tmp;
			for (int j=0;j+(1<<i)<v.size();j++)
			tmp.push_back(v[j]^v[j+(1<<i)]);
			v=tmp;
		}
	}
	cout << v[0];
}