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

const int MAXN = 1e6 + 5;

int N;
char s[MAXN];
int nxt[MAXN];

void load() {
	scanf("%d%s", &N, s);
}

int parity() {
	int res = 0;
	for (int i = 0; i < N - 1; i++)
		if ((N - 2 & i) == i)
			res ^= nxt[i] & 1;
	return res;
}

int solve() {
	bool one = false;
	for (int i = 0; i < N - 1; i++) {
		nxt[i] = abs((int)s[i] - (int)s[i + 1]);
		one |= nxt[i] == 1;
	}
	if (one)
		return parity();
	for (int i = 0; i < N - 1; i++)
		nxt[i] /= 2;
	return 2 * parity();
}

int main() {
	load();
	printf("%d\n", solve());
	return 0;
}
### Prompt

Develop a solution in cpp to the problem described below:

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 MAXN = 1e6 + 5;

int N;
char s[MAXN];
int nxt[MAXN];

void load() {
	scanf("%d%s", &N, s);
}

int parity() {
	int res = 0;
	for (int i = 0; i < N - 1; i++)
		if ((N - 2 & i) == i)
			res ^= nxt[i] & 1;
	return res;
}

int solve() {
	bool one = false;
	for (int i = 0; i < N - 1; i++) {
		nxt[i] = abs((int)s[i] - (int)s[i + 1]);
		one |= nxt[i] == 1;
	}
	if (one)
		return parity();
	for (int i = 0; i < N - 1; i++)
		nxt[i] /= 2;
	return 2 * parity();
}

int main() {
	load();
	printf("%d\n", solve());
	return 0;
}
```