#include <bits/stdc++.h>

using namespace std;
const int N = 1000010;
int _w;

int C( int n, int m ) {
	return (n|m) == n;
}

int n, a[N], cnt[3];
char s[N];

int main() {
	cin >> n;
	cin >> (s+1);
	for( int i = 1; i <= n; ++i ) {
		a[i] = s[i] - '0' - 1;
		++cnt[a[i]];
	}
	if( cnt[1] == 0 ) {
		for( int i = 1; i <= n; ++i )
			if( a[i] == 2 )
				a[i] = 1;
	} else {
		for( int i = 1; i <= n; ++i )
			if( a[i] == 2 )
				a[i] = 0;
	}
	int ans = 0;
	for( int i = 1; i <= n; ++i )
		ans = (ans + a[i] * C(n-1, i-1)) & 1;
	if( cnt[1] == 0 ) ans *= 2;
	printf( "%d\n", ans );
	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 N = 1000010;
int _w;

int C( int n, int m ) {
	return (n|m) == n;
}

int n, a[N], cnt[3];
char s[N];

int main() {
	cin >> n;
	cin >> (s+1);
	for( int i = 1; i <= n; ++i ) {
		a[i] = s[i] - '0' - 1;
		++cnt[a[i]];
	}
	if( cnt[1] == 0 ) {
		for( int i = 1; i <= n; ++i )
			if( a[i] == 2 )
				a[i] = 1;
	} else {
		for( int i = 1; i <= n; ++i )
			if( a[i] == 2 )
				a[i] = 0;
	}
	int ans = 0;
	for( int i = 1; i <= n; ++i )
		ans = (ans + a[i] * C(n-1, i-1)) & 1;
	if( cnt[1] == 0 ) ans *= 2;
	printf( "%d\n", ans );
	return 0;
}

```