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 <iostream>
#include <cstdio>
using namespace std;

typedef long long ll;
ll n, m, s, cnt, a[1000005];
string ta;
int main()
{
	ll i, j, t;
	cin >> n;
	cin >> ta;
	for (i = 0; i < n; i++) {
		a[i] = ta[i] - '1';
		if (a[i] == 1) cnt++;
	}
	for (i = 0; i < n; i++) {
		j = n - i - 1;
		t = (i ^ j);
		if (t == n - 1) s += a[i];
	}
	if (s % 2) {
		cout << 1;
		return 0;
	}
	if (cnt > 0) {
		cout << 0;
		return 0;
	}
	for (i = 0; i < n; i++) {
		a[i] /= 2;
	}
	s = 0;
	for (i = 0; i < n; i++) {
		j = n - i - 1;
		t = (i ^ j);
		if (t == n - 1) s += a[i];
	}
	if (s % 2) cout << 2;
	else cout << 0;
    return 0;
}