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: Accepted)

#include <bits/stdc++.h>
#define PB push_back
#define MP make_pair
#define F first
#define S second
#define SZ(x) ((int)(x).size())
#define ALL(x) (x).begin(),(x).end()
#ifdef _DEBUG_
  #define debug(...) printf(__VA_ARGS__)
#else
  #define debug(...) (void)0
#endif
using namespace std;
typedef long long ll;
typedef pair<int,int> PII;
typedef vector<int> VI;

const int MAX = 1e6 + 100;
int cnt2[MAX];

int main() {
  cnt2[0] = 0;
  for (int i = 1; i < MAX; i++) {
    int t = i, c = 0;
    while (t % 2 == 0 && t > 0) {
      t /= 2;
      c++;
    }
    cnt2[i] = cnt2[i - 1] + c;
  }

  int N;
  cin >> N;
  string S;
  cin >> S;
  for (char &c : S) {
    c--;
  }
  bool ex1 = false;
  for (char c : S) {
    if (c == '1')
      ex1 = true;
  }

  if (ex1) {
    // 0 or 1
    for (char &c : S) {
      if (c == '2')
        c = '0';
    }
  }
  int r = 0;
  for (int i = 0; i < SZ(S); i++) {
    assert(cnt2[SZ(S) - 1] - cnt2[i] - cnt2[SZ(S) - 1 - i] >= 0);
    if (S[i] > '0') {
      if (cnt2[SZ(S) - 1] - cnt2[i] - cnt2[SZ(S) - 1 - i] == 0)
        r ^= 1;
    }
    debug("%d %d -> %d\n", SZ(S), i, cnt2[SZ(S) - 1] - cnt2[i] - cnt2[SZ(S) - 1 - i] == 0);
  }
  if (r) {
    if (ex1)
      puts("1");
    else
      puts("2");
  } else {
    puts("0");
  }
  return 0;
}