#include<iostream>
using namespace std;
int N;
bool isone(string s)
{
	int N=s.size()-1;
	int p2=0,ret=0;
	for(int i=0;i<=N;i++)
	{
		int si=s[N-i]-'0';
		if(i>0)
		{
			int x=i;
			while(x%2==0)x/=2,p2--;
			x=N-i+1;
			while(x%2==0)x/=2,p2++;
		}
		if(p2==0)ret=(ret+si)%2;
	}
	return ret%2;
}
int main()
{
	string s;
	cin>>N>>s;
	for(int i=0;i<N;i++)s[i]--;
	if(isone(s))cout<<1<<endl;
	else
	{
		string t=s;
		bool flag=true;
		for(int i=0;i<N;i++)
		{
			if(t[i]=='2')t[i]='1';
			else if(t[i]=='1')flag=false;
		}
		if(flag&&isone(t))cout<<2<<endl;
		else cout<<0<<endl;
	}
}

### Prompt

Create a solution in Cpp for 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<iostream>
using namespace std;
int N;
bool isone(string s)
{
	int N=s.size()-1;
	int p2=0,ret=0;
	for(int i=0;i<=N;i++)
	{
		int si=s[N-i]-'0';
		if(i>0)
		{
			int x=i;
			while(x%2==0)x/=2,p2--;
			x=N-i+1;
			while(x%2==0)x/=2,p2++;
		}
		if(p2==0)ret=(ret+si)%2;
	}
	return ret%2;
}
int main()
{
	string s;
	cin>>N>>s;
	for(int i=0;i<N;i++)s[i]--;
	if(isone(s))cout<<1<<endl;
	else
	{
		string t=s;
		bool flag=true;
		for(int i=0;i<N;i++)
		{
			if(t[i]=='2')t[i]='1';
			else if(t[i]=='1')flag=false;
		}
		if(flag&&isone(t))cout<<2<<endl;
		else cout<<0<<endl;
	}
}

```