#include<bits/stdc++.h>
#define T(x,y) (Num(x)-Num(x-(y))-Num(y))
using namespace std;
int n,a[1000010],tag=1,ans;
char c[1000010];
int Num(int x){
	int ret=0;
	for(int i=2;i<=x;i<<=1)ret+=x/i;
	return ret;
}
int main(){
	scanf("%d%s",&n,c+1);
	for(int i=1;i<n;++i)a[i]=abs(c[i]-c[i+1]),tag&=(a[i]!=1);
	--n;
	if(tag){
		for(int i=1;i<=n;++i)if(a[i])ans^=!T(n-1,n-i);
		return putchar(ans?'2':'0'),0;
	}
	for(int i=1;i<=n;++i)if(a[i]==1)ans^=!T(n-1,n-i);
	return putchar(ans?'1':'0'),0;
	return 0;
}
### Prompt

Construct a cpp code solution to the problem outlined:

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 T(x,y) (Num(x)-Num(x-(y))-Num(y))
using namespace std;
int n,a[1000010],tag=1,ans;
char c[1000010];
int Num(int x){
	int ret=0;
	for(int i=2;i<=x;i<<=1)ret+=x/i;
	return ret;
}
int main(){
	scanf("%d%s",&n,c+1);
	for(int i=1;i<n;++i)a[i]=abs(c[i]-c[i+1]),tag&=(a[i]!=1);
	--n;
	if(tag){
		for(int i=1;i<=n;++i)if(a[i])ans^=!T(n-1,n-i);
		return putchar(ans?'2':'0'),0;
	}
	for(int i=1;i<=n;++i)if(a[i]==1)ans^=!T(n-1,n-i);
	return putchar(ans?'1':'0'),0;
	return 0;
}
```