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

int main(){
	int n;
	cin >> n;
	string s;
	cin >> s;
	int a[n-1];
	for(int i =0;i<n-1;i++)
		a[i] = abs(s[i]-s[i+1]);

	int cnt[3];
	memset(cnt,0,sizeof(cnt));
	for(int i =0;i<n-1;i++)
		cnt[a[i]]++;
	int to_check = 1;
	if(cnt[1]==0){
		to_check = 2;
		for(int i =0;i<n-1;i++)
			a[i]>>=1;
	}

	int res = 0;
	for(int i =0;i<n-1;i++){
		if(((n-2)&i) == i) // applying lucas theorem for mod 2
			res^=a[i];
	}
	// cout << res << to_check << endl;
	cout << (res%2)*to_check << endl;
}
### Prompt

Please provide a cpp coded solution 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;

int main(){
	int n;
	cin >> n;
	string s;
	cin >> s;
	int a[n-1];
	for(int i =0;i<n-1;i++)
		a[i] = abs(s[i]-s[i+1]);

	int cnt[3];
	memset(cnt,0,sizeof(cnt));
	for(int i =0;i<n-1;i++)
		cnt[a[i]]++;
	int to_check = 1;
	if(cnt[1]==0){
		to_check = 2;
		for(int i =0;i<n-1;i++)
			a[i]>>=1;
	}

	int res = 0;
	for(int i =0;i<n-1;i++){
		if(((n-2)&i) == i) // applying lucas theorem for mod 2
			res^=a[i];
	}
	// cout << res << to_check << endl;
	cout << (res%2)*to_check << endl;
}
```