#include<bits/stdc++.h>
#define ll long long
using namespace std;
#define gc getchar
inline ll read(){
    char ch=gc();
    while (!isdigit(ch)) ch=gc();
    return ch-'0';
}
ll a[1111111],n,b[1111111];
signed main(){
	cin>>n;
	for (int i=1;i<=n;i++) a[i]=read(); 
	n--;
	for (int i=1;i<=n;i++) b[i]=abs(a[i+1]-a[i]);
	for (int i=1;i<=n;i++) a[i]=b[i];
	ll _=0;
	bool flag1=0;
	for (int i=1;i<=n;i++){
		_=(_+((((n-1)&(i-1))==i-1)?a[i]:0))&1;
		flag1|=(a[i]==1);
	}
	if (_==1) puts("1");
	else{
		if (flag1) puts("0"); 
		else{
			_=0;
			for (int i=1;i<=n;i++){
				_=(_+((((n-1)&(i-1))==i-1)?a[i]/2:0))&1;
			}
			puts(_==0?"0":"2");
		}
	}
    return 0;
}

### Prompt

Your task is to create 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>
#define ll long long
using namespace std;
#define gc getchar
inline ll read(){
    char ch=gc();
    while (!isdigit(ch)) ch=gc();
    return ch-'0';
}
ll a[1111111],n,b[1111111];
signed main(){
	cin>>n;
	for (int i=1;i<=n;i++) a[i]=read(); 
	n--;
	for (int i=1;i<=n;i++) b[i]=abs(a[i+1]-a[i]);
	for (int i=1;i<=n;i++) a[i]=b[i];
	ll _=0;
	bool flag1=0;
	for (int i=1;i<=n;i++){
		_=(_+((((n-1)&(i-1))==i-1)?a[i]:0))&1;
		flag1|=(a[i]==1);
	}
	if (_==1) puts("1");
	else{
		if (flag1) puts("0"); 
		else{
			_=0;
			for (int i=1;i<=n;i++){
				_=(_+((((n-1)&(i-1))==i-1)?a[i]/2:0))&1;
			}
			puts(_==0?"0":"2");
		}
	}
    return 0;
}

```