#include<cstdio>
#include<algorithm>
using namespace std;
typedef long long ll;
const int MAXN = 1e6 + 5;

char s[MAXN];
int a[MAXN];

int c(int n,int m){ return (n|m)==n;}

int main(void)
{
	int n;
	scanf("%d%s",&n,s+1);
	for(int i=1; i<=n; ++i) a[i]=s[i]-'1';
	
	bool flag=1;
	for(int i=1; i<=n; ++i)
		if(a[i]==1){ flag=0; break;}
	
	if(flag)
	{
		for(int i=1; i<=n; ++i)
			a[i]>>=1;
	}
	else
	{
		for(int i=1; i<=n; ++i)
			a[i]&=1;
	}
	
	int ans=0;
	for(int i=1; i<=n; ++i)
		ans ^= a[i]&c(n-1,i-1);
	if(flag) ans<<=1;
	printf("%d",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<cstdio>
#include<algorithm>
using namespace std;
typedef long long ll;
const int MAXN = 1e6 + 5;

char s[MAXN];
int a[MAXN];

int c(int n,int m){ return (n|m)==n;}

int main(void)
{
	int n;
	scanf("%d%s",&n,s+1);
	for(int i=1; i<=n; ++i) a[i]=s[i]-'1';
	
	bool flag=1;
	for(int i=1; i<=n; ++i)
		if(a[i]==1){ flag=0; break;}
	
	if(flag)
	{
		for(int i=1; i<=n; ++i)
			a[i]>>=1;
	}
	else
	{
		for(int i=1; i<=n; ++i)
			a[i]&=1;
	}
	
	int ans=0;
	for(int i=1; i<=n; ++i)
		ans ^= a[i]&c(n-1,i-1);
	if(flag) ans<<=1;
	printf("%d",ans);
	return 0;
}
```