#include <cstdio>
#include <cstring>
#include <algorithm>
using namespace std;

const int MAXN = 1000000;

int C(int n, int m) {
	if( m == 0 ) return 1;
	if( (n & 1) < (m & 1) ) return 0;
	return C(n / 2, m / 2);
}
int abs(int x) {
	return x >= 0 ? x : -x;
}

int N; char s[MAXN + 5];
int a[MAXN + 5];
int main() {
	scanf("%d%s", &N, s);
	bool flag = false;
	for(int i=1;i<N;i++) {
		a[i] = abs(s[i - 1] - s[i]);
		if( a[i] == 1 ) flag = true;
	}
	if( flag ) {
		int ans = 0;
		for(int i=1;i<N;i++)
			if( C(N - 2, i - 1) && a[i] == 1 ) ans ^= 1;
		printf("%d\n", ans);
	}
	else {
		int ans = 0;
		for(int i=1;i<N;i++)
			if( C(N - 2, i - 1) && a[i] == 2 ) ans ^= 1;
		printf("%d\n", ans*2);
	}
}
### 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 <cstdio>
#include <cstring>
#include <algorithm>
using namespace std;

const int MAXN = 1000000;

int C(int n, int m) {
	if( m == 0 ) return 1;
	if( (n & 1) < (m & 1) ) return 0;
	return C(n / 2, m / 2);
}
int abs(int x) {
	return x >= 0 ? x : -x;
}

int N; char s[MAXN + 5];
int a[MAXN + 5];
int main() {
	scanf("%d%s", &N, s);
	bool flag = false;
	for(int i=1;i<N;i++) {
		a[i] = abs(s[i - 1] - s[i]);
		if( a[i] == 1 ) flag = true;
	}
	if( flag ) {
		int ans = 0;
		for(int i=1;i<N;i++)
			if( C(N - 2, i - 1) && a[i] == 1 ) ans ^= 1;
		printf("%d\n", ans);
	}
	else {
		int ans = 0;
		for(int i=1;i<N;i++)
			if( C(N - 2, i - 1) && a[i] == 2 ) ans ^= 1;
		printf("%d\n", ans*2);
	}
}
```