Problem:
Score : 700 points

Problem Statement

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}.

Sample Input 1

4
1231

Sample Output 1

1

x_{1,1},x_{1,2},x_{1,3},x_{1,4} are respectively 1,2,3,1.

x_{2,1},x_{2,2},x_{2,3} are respectively |1-2| = 1,|2-3| = 1,|3-1| = 2.

x_{3,1},x_{3,2} are respectively |1-1| = 0,|1-2| = 1.

Finally, x_{4,1} = |0-1| = 1, so the answer is 1.

Sample Input 2

10
2311312312

Sample Output 2

0

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef vector<ll> vec;
typedef vector<vec> mat;
typedef pair<ll,ll> pll;
const ll mod=1e9+7;
//const ll mod=998244353;
const ll inf=1LL<<62;

ll fact(ll n) {
  ll res=0;
  while(n/2) {
    res+=n/2;
    n/=2;
  }
  return res;
}

ll comb(ll n, ll k) {
  ll res=fact(n)-fact(k)-fact(n-k);
  if(res) res=0;
  else res=1;
  return res;
}

int main() {
  ll n;
  cin >> n;
  string s;
  cin >> s;
  if(n<=4) {
    mat a(n,vec(n));
    for(ll i=0;i<n;i++) {
      a[0][i]=s[i]-'0';
    }
    for(ll i=1;i<n;i++) {
      for(ll j=0;j<n-i;j++) {
        a[i][j]=abs(a[i-1][j]-a[i-1][j+1]);
      }
    }
    cout << a[n-1][0] << endl;
  }
  else {
    ll sum=0;
    for(ll i=0;i<n;i++) {
      ll idx=s[i]-'0';
      sum+=idx*comb(n-1,i)%2;
      sum%=2;
    }
    cout << sum << endl;
  }
}