#include <bits/stdc++.h>
using namespace std;
#define mod 998244353
#define MOD 1000000007
#define inf 0x3f3f3f3f
#define linf 0x3f3f3f3f3f3f3f3fll
typedef long long ll;
typedef pair<int,int> pii;
typedef unsigned long long ull;
const int maxn=1e6+10;
int cn[maxn];
int n;
char s[maxn];
bool check2()
{
	for(int i=0;i<n;i++)if(s[i]=='2')return 0;
	int c2=0;
	for(int i=0;i<n;i++)
	{
		if(cn[i]&&(s[i]=='1'))c2^=1;
	}
	return c2;
}
int main()
{
	scanf("%d",&n);
	scanf("%s",s);
	int sum=0;
	for(int i=0;i<n;i++)
	{
		cn[i]=((n-1)&i)==i;
		if(cn[i]&&(s[i]!='2'))sum^=1;
	}
	if(sum==1)
	{
		printf("1\n");
	}
	else
	{
		if(check2())printf("2\n");
		else printf("0\n");
	}
	return 0;
	
}
### Prompt

Please provide a cpp coded solution to the problem described below:

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>
using namespace std;
#define mod 998244353
#define MOD 1000000007
#define inf 0x3f3f3f3f
#define linf 0x3f3f3f3f3f3f3f3fll
typedef long long ll;
typedef pair<int,int> pii;
typedef unsigned long long ull;
const int maxn=1e6+10;
int cn[maxn];
int n;
char s[maxn];
bool check2()
{
	for(int i=0;i<n;i++)if(s[i]=='2')return 0;
	int c2=0;
	for(int i=0;i<n;i++)
	{
		if(cn[i]&&(s[i]=='1'))c2^=1;
	}
	return c2;
}
int main()
{
	scanf("%d",&n);
	scanf("%s",s);
	int sum=0;
	for(int i=0;i<n;i++)
	{
		cn[i]=((n-1)&i)==i;
		if(cn[i]&&(s[i]!='2'))sum^=1;
	}
	if(sum==1)
	{
		printf("1\n");
	}
	else
	{
		if(check2())printf("2\n");
		else printf("0\n");
	}
	return 0;
	
}
```