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

#pragma GCC optimize("Ofast,no-stack-protector,unroll-loops,fast-math")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
#define IOS ios::sync_with_stdio(0), cin.tie(0), cout.tie(0)
#define F first
#define S second

const int maxn = 1e6 + 12;
int a[maxn], n, C = 0, ans;
string s;

int main() {
	cin >> n >> s;
	for (int i = 0; i < n; i++) {
		a[i] = s[i] - '0' - 1;
		if(!C && a[i] == 1) C = 1;
	}
	for (int i = 0; i < n; i++) if(C) a[i] %= 2;
	for (int i = 0; i < n; i++) if(((n - 1) & i) == i) ans ^= a[i];
	cout << ans;
	return 0;
}	

### Prompt

Please formulate a cpp solution to the following problem:

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;

#pragma GCC optimize("Ofast,no-stack-protector,unroll-loops,fast-math")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
#define IOS ios::sync_with_stdio(0), cin.tie(0), cout.tie(0)
#define F first
#define S second

const int maxn = 1e6 + 12;
int a[maxn], n, C = 0, ans;
string s;

int main() {
	cin >> n >> s;
	for (int i = 0; i < n; i++) {
		a[i] = s[i] - '0' - 1;
		if(!C && a[i] == 1) C = 1;
	}
	for (int i = 0; i < n; i++) if(C) a[i] %= 2;
	for (int i = 0; i < n; i++) if(((n - 1) & i) == i) ans ^= a[i];
	cout << ans;
	return 0;
}	

```