#include <bits/stdc++.h>
using namespace std;

const int mod = 2;

char s[1000010];

int lucas(int a, int b) {
	if (a < 2 && b < 2) {
		if (a == 0 && b == 1) return 0;
		return 1;
	}
	return lucas(a >> 1, b >> 1) * lucas(a & 1, b & 1);
}

int main () {
	int n; scanf("%d", &n);
	scanf("%s", s);
	int pd = 0;
	for (int i = 0; i < n; i++) {
		s[i]--;
		if (s[i] == '1') pd = 1;
	}
	if (pd) {
		int ans = 0;
		for (int i = 0; i < n; i++) {
			if (s[i] == '1') {
				ans ^= lucas(n - 1, i);
			}
		}
		printf("%d\n", ans ? 1 : 0);
	} else {
		int ans = 0;
		for (int i = 0; i < n; i++) {
			if (s[i] == '2') {
				ans ^= lucas(n - 1, i);
			}
		}
		printf("%d\n", ans ? 2 : 0);
	}
	return 0;
}

### Prompt

Construct a cpp code solution to the problem outlined:

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

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;

const int mod = 2;

char s[1000010];

int lucas(int a, int b) {
	if (a < 2 && b < 2) {
		if (a == 0 && b == 1) return 0;
		return 1;
	}
	return lucas(a >> 1, b >> 1) * lucas(a & 1, b & 1);
}

int main () {
	int n; scanf("%d", &n);
	scanf("%s", s);
	int pd = 0;
	for (int i = 0; i < n; i++) {
		s[i]--;
		if (s[i] == '1') pd = 1;
	}
	if (pd) {
		int ans = 0;
		for (int i = 0; i < n; i++) {
			if (s[i] == '1') {
				ans ^= lucas(n - 1, i);
			}
		}
		printf("%d\n", ans ? 1 : 0);
	} else {
		int ans = 0;
		for (int i = 0; i < n; i++) {
			if (s[i] == '2') {
				ans ^= lucas(n - 1, i);
			}
		}
		printf("%d\n", ans ? 2 : 0);
	}
	return 0;
}

```