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 (Clang 3.8.0) (judge verdict: Accepted)

#include <iostream>
#include <cmath>
#include <string>
#include <vector>

using namespace std;
using ll = long long int;


ll cnt2(ll n) {
  return 0;
}

ll comb(ll n, ll r) {
  for (ll base = 60; base >= 1; base--) {
    if (r > n) return 0;
    if (n >= (1LL << base)) n %= (1LL << base);
    if (r >= (1LL << base)) r %= (1LL << base);
  }

  if (n == 0 && r == 1) {
    return 0;
  } else {
    return 1;
  }
}


int main() {
  ll N;
  string A;
  
  cin >> N >> A;

  vector<ll> a;

  char current = A[0];


  // for (int i = 0; i < 30; i++) {
  //   for (int r = 0; r <= i; r++) {
  //     cout << comb(i, r) << " ";
  //   }
  //   cout << endl;
  // }

  for (ll i = 1; i < N; i++) {
    a.push_back(abs(A[i] - current));
    current = A[i];
  }


  // 0 or 2
  bool is_zero_or_two = true;
  for (ll c : a) {
    if (c == 1) {
      is_zero_or_two = false;
    }
  }

  // 0 or 2
  ll mult = 1;
  if (is_zero_or_two) {
    mult = 2;
    for (int i = 0; i < N - 1; i++) {
      a[i] /= 2;
    }
  }

  ll res = 0;

  for (int i = 0; i < N - 1; i++) {
    ll com = comb(N - 2, i);
    res = (res + com * a[i]) % 2;
  }

  cout << res * mult << endl;

  return 0;
}