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 std::pair;
const int N = 1e6 + 5;
int n, tot, a[N]; 
char s[N];

int main()
{
	scanf("%d%s", &n, s);
	--n;
	for (int i = 0; i <= n; ++i)
		a[i] = s[i] - '0' - 1;
	for (int i = 0; i <= n; ++i)
		if ((n & i) == i)
			tot = tot + a[i] & 1;
	if (tot)
		puts("1");
	else
	{
		bool flag = false;
		for (int i = 0; i <= n; ++i)
			if (a[i] == 1)
			{
				puts("0");
				flag = true;
				break ;
			}
		if (!flag)
		{
			tot = 0;
			for (int i = 0; i <= n; ++i)
				if ((n & i) == i)
					tot = tot + (a[i] >> 1) & 1;
			printf("%d\n", tot << 1);
		}
	}
}