#include<cstdio>
typedef long long LL;
using namespace std;
const int N=1e6+5;
int n;
char s[N];
inline bool chk(){
	int u=0,v=0,w=0;
	for(int i=0;i<=n;++i){
		if(u==v)w=(w+s[i])&1;
		if(i<n)u+=__builtin_ctz(n-i),v+=__builtin_ctz(i+1);
	}
	return w;
}
int main(){
	scanf("%d%s",&n,s);
	if(!--n)putchar(*s);else{
		for(int i=0;i<=n;++i)--s[i];
		if(chk())putchar(49);else{
			bool ok=1;
			for(int i=0;i<=n;++i)
			if(s[i]==49)ok=0;else if(s[i]==50)--s[i];
			if(ok&&chk())putchar(50);else putchar(48);
		}
	}
	return 0;
}
### 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<cstdio>
typedef long long LL;
using namespace std;
const int N=1e6+5;
int n;
char s[N];
inline bool chk(){
	int u=0,v=0,w=0;
	for(int i=0;i<=n;++i){
		if(u==v)w=(w+s[i])&1;
		if(i<n)u+=__builtin_ctz(n-i),v+=__builtin_ctz(i+1);
	}
	return w;
}
int main(){
	scanf("%d%s",&n,s);
	if(!--n)putchar(*s);else{
		for(int i=0;i<=n;++i)--s[i];
		if(chk())putchar(49);else{
			bool ok=1;
			for(int i=0;i<=n;++i)
			if(s[i]==49)ok=0;else if(s[i]==50)--s[i];
			if(ok&&chk())putchar(50);else putchar(48);
		}
	}
	return 0;
}
```