#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
const int maxn=1e6+5;
const int mod=2;
char buff[maxn];
int cnt[maxn],sum[maxn];
int main() {
    int n;cin>>n>>(buff+1);bool one=0;
    for(int i=1;i<=n;i++) {
        buff[i]-='1';if(buff[i]==1) one=1;
        if(i%2==0) cnt[i]=cnt[i/2]+1;
        sum[i]=sum[i-1]+cnt[i];
    }
    if(!one) for(int i=1;i<=n;i++) buff[i]/=2;
    int ans=0;
    for(int i=1;i<=n;i++) if(sum[n-1]==sum[i-1]+sum[n-i]) ans=ans+buff[i];
    ans%=2;
    cout<<ans*(one?1:2)<<endl;
    return 0;
}
### Prompt

Generate 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 <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
const int maxn=1e6+5;
const int mod=2;
char buff[maxn];
int cnt[maxn],sum[maxn];
int main() {
    int n;cin>>n>>(buff+1);bool one=0;
    for(int i=1;i<=n;i++) {
        buff[i]-='1';if(buff[i]==1) one=1;
        if(i%2==0) cnt[i]=cnt[i/2]+1;
        sum[i]=sum[i-1]+cnt[i];
    }
    if(!one) for(int i=1;i<=n;i++) buff[i]/=2;
    int ans=0;
    for(int i=1;i<=n;i++) if(sum[n-1]==sum[i-1]+sum[n-i]) ans=ans+buff[i];
    ans%=2;
    cout<<ans*(one?1:2)<<endl;
    return 0;
}
```