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

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define rep(i, n) for (ll i = 0; i < (ll)(n); i++)
ll ans = 0;

int main()
{
ll n ;
cin >> n ;
string s ;
cin >> s ;
vector<ll> v;
rep(i,n){
  v.push_back(s[i]-'1');
}
bool ok=1;
rep(i,n)if(v[i]==1)ok=0;
if(ok)rep(i,n)v[i]/=2;
ll sum=0;
rep(i,n-1){
  sum+=__builtin_ffsll(n-1-i)-__builtin_ffsll(i+1);
  if(sum==0)ans=(ans+v[i+1])%2;
}
ans=(ans+v[0])%2;
if(ok)ans*=2;
cout << ans << endl;
return 0;
}