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: Time Limit Exceeded)

#include <bits/stdc++.h>
using namespace std;

#define rep(i, a, b) for (int i = (a), i##end = (b); i <= i##end; ++i)
#define per(i, a, b) for (int i = (a), i##end = (b); i >= i##end; --i)

mt19937 Rnd(chrono::high_resolution_clock::now().time_since_epoch().count());

template <typename T>
inline void chkmax(T &x, T y) { if (x < y) x = y; }

template <typename T>
inline void chkmin(T &x, T y) { if (x > y) x = y; }

inline int read() {
  #define nc getchar()
  int x = 0;
  char c = nc;
  while (c < 48) c = nc;
  while (c > 47) x = (x << 3) + (x << 1) + (c ^ 48), c = nc;
  return x;
  #undef nc
}

typedef long long ll;
const int maxn = 1e6 + 10;
int n, a[maxn], val[maxn];

inline int abso(int x) {
  return x < 0 ? -x : x;
}

int main() {
  cin >> n;
  rep(i, 1, n) scanf("%1d", val + i);
  int len = 1;
  rep(T, 2, n) {
    bool flg = 1;
    rep(i, 1, n - T + 1) val[i] = abso(val[i] - val[i + 1]), flg &= val[i] < 2;
    if (flg) {
      len = n - T + 1; break;
    }
  }
  if (len == 1) {
    cout << val[1] << endl;
    return 0;
  }
  int res = 0;
  rep(i, 1, len) if (val[i]) {
    res ^= (((len - 1) & (i - 1)) == (i - 1));
  }
  cout << res << endl;
  return 0;
}