#include<bits/stdc++.h>

using namespace std;

#define N 1000005

int n, a[N];

string s;

int get()
{
	int res = 0;
	for(int i = 0; i <= n; i++)
	{
		int now = a[i] % 2;
		if(now && ((n & i) == i)) res ^= 1;
	}
	return res;
}

int main()
{
	cin >> n >> s;
	n--;
	for(int i = 0; i <= n; i++)
		a[i] = s[i] - '1';
	if(get()) cout << 1 << endl;
	else
	{
		for(int i = 0; i <= n; i++)
			if(a[i] == 1) 
			{
				cout << 0 << endl;
				return 0;
			}
		for(int i = 0; i <= n; i++)
			a[i] /= 2;
		if(get()) cout << 2 << endl;
		else cout << 0 << endl;
	}
	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;

#define N 1000005

int n, a[N];

string s;

int get()
{
	int res = 0;
	for(int i = 0; i <= n; i++)
	{
		int now = a[i] % 2;
		if(now && ((n & i) == i)) res ^= 1;
	}
	return res;
}

int main()
{
	cin >> n >> s;
	n--;
	for(int i = 0; i <= n; i++)
		a[i] = s[i] - '1';
	if(get()) cout << 1 << endl;
	else
	{
		for(int i = 0; i <= n; i++)
			if(a[i] == 1) 
			{
				cout << 0 << endl;
				return 0;
			}
		for(int i = 0; i <= n; i++)
			a[i] /= 2;
		if(get()) cout << 2 << endl;
		else cout << 0 << endl;
	}
	return 0;
}
```