#include<cstdio>
#include<cstring>
#include<cmath>
#include<algorithm>
using namespace std;
const int N=1000005;
int n,i,j,k,a[N],cnt,tot;
char s[N];
int Abs(int a)
{
	return a>0?a:-a;
}
int C(int n,int m)
{
	return (m|n)==n;
	if(n%2<m%2)
		return 0;
	if(n==0)
		return 1;
	return C(n/2,m/2);
}
int main()
{
	scanf("%d%s",&n,s+1);
	for(i=1;i<n;++i)
		a[i]=Abs(s[i]-s[i+1]);
	--n;
	for(i=1;i<=n;++i)
		if(a[i]==1)
			break;
	if(i<=n)
	{
		k=1;
		for(i=1;i<=n;++i)
			if(a[i]==2)
				a[i]=0;
	}
	else
	{
		k=2;
		for(i=1;i<=n;++i)
			if(a[i]==2)
				a[i]=1;
	}
	j=0;
	for(i=1;i<=n;++i)
		j=(j+1ll*C(n-1,i-1)*a[i])%2;
	printf("%d",j*k);
	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<cstdio>
#include<cstring>
#include<cmath>
#include<algorithm>
using namespace std;
const int N=1000005;
int n,i,j,k,a[N],cnt,tot;
char s[N];
int Abs(int a)
{
	return a>0?a:-a;
}
int C(int n,int m)
{
	return (m|n)==n;
	if(n%2<m%2)
		return 0;
	if(n==0)
		return 1;
	return C(n/2,m/2);
}
int main()
{
	scanf("%d%s",&n,s+1);
	for(i=1;i<n;++i)
		a[i]=Abs(s[i]-s[i+1]);
	--n;
	for(i=1;i<=n;++i)
		if(a[i]==1)
			break;
	if(i<=n)
	{
		k=1;
		for(i=1;i<=n;++i)
			if(a[i]==2)
				a[i]=0;
	}
	else
	{
		k=2;
		for(i=1;i<=n;++i)
			if(a[i]==2)
				a[i]=1;
	}
	j=0;
	for(i=1;i<=n;++i)
		j=(j+1ll*C(n-1,i-1)*a[i])%2;
	printf("%d",j*k);
	return 0;
}

```