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;

using ll = long long;

template <typename T>
void printv(const vector<T> &v) {
  int sz = v.size();
  for (int i = 0; i < sz; i++) {
    cout << v[i] << " \n"[i == sz - 1];
  }
}

const int MAX_N = 1000010;
// two[i] := i! が 2 で割れる回数
vector<ll> two(MAX_N);

// nCr が 2 で割れる回数
ll comb_two(int n, int r) {
  assert(two[n] - two[r] - two[n - r] >= 0);
  return two[n] - two[r] - two[n - r];
}

int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);

  for (int i = 1; i < MAX_N; i++) {
    int cnt = 0;
    ll val = i;
    while (val % 2 == 0) {
      cnt++;
      val /= 2;
    }
    two[i] = two[i - 1] + cnt;
  }
  int n;
  cin >> n;
  string s;
  cin >> s;
  bool one = false;
  vector<ll> a(n);
  for (int i = 0; i < n; i++) {
    a[i] = s[i] - '1';
    if (a[i] == 1) one = true;
  }
  ll sum = 0;
  for (int i = 0; i < n; i++) {
    // n-1 C i
    if (comb_two(n - 1, i) == 0) sum = (sum + 1) % 2;
  }
  if (sum) {
    cout << 1 << endl;
    return 0;
  }
  if (one) {
    cout << 0 << endl;
    return 0;
  }
  for (int i = 0; i < n; i++) {
    a[i] /= 2;
  }
  sum = 0;
  for (int i = 0; i < n; i++) {
    if (comb_two(n - 1, i) == 0) sum = (sum + 1) % 2;
  }
  if (sum)
    cout << 2 << endl;
  else
    cout << 0 << endl;
}