#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
int n,sum,ct1,f[1000005];
char s[1000005];
int getans(int n,int m)
{
	if(n<m) return 0;
	if(n<=1) return 1;
	return getans(n/2,m/2)*getans(n%2,m%2); 
}
int main()
{
	scanf("%d%s",&n,s+1);
	for(int i=1;i<=n;i++)
		f[i]=getans(n-1,i-1);
	for(int i=1;i<=n;i++)
		ct1+=(s[i]=='2');
	int ct=0;
	if(ct1)
	{
		for(int i=1;i<=n;i++)
			if(f[i]) ct+=(s[i]=='2');
		if(ct%2) printf("1");
		else printf("0");
	}
	else
	{
		for(int i=1;i<=n;i++)
			if(f[i]) ct+=(s[i]=='3');
		if(ct%2) printf("2");
		else printf("0");
	}
	return 0;
}
### Prompt

Please create a solution in Cpp 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<algorithm>
using namespace std;
int n,sum,ct1,f[1000005];
char s[1000005];
int getans(int n,int m)
{
	if(n<m) return 0;
	if(n<=1) return 1;
	return getans(n/2,m/2)*getans(n%2,m%2); 
}
int main()
{
	scanf("%d%s",&n,s+1);
	for(int i=1;i<=n;i++)
		f[i]=getans(n-1,i-1);
	for(int i=1;i<=n;i++)
		ct1+=(s[i]=='2');
	int ct=0;
	if(ct1)
	{
		for(int i=1;i<=n;i++)
			if(f[i]) ct+=(s[i]=='2');
		if(ct%2) printf("1");
		else printf("0");
	}
	else
	{
		for(int i=1;i<=n;i++)
			if(f[i]) ct+=(s[i]=='3');
		if(ct%2) printf("2");
		else printf("0");
	}
	return 0;
}
```