Problem: Toad Mikhail has an array of 2^k integers a_1, a_2, …, a_{2^k}.

Find two permutations p and q of integers 0, 1, …, 2^k-1, such that a_i is equal to p_i ⊕ q_i for all possible i, or determine there are no such permutations. Here ⊕ denotes the [bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR).

Input

The first line contains one integer k (2 ≤ k ≤ 12), denoting that the size of the array is 2^k.

The next line contains 2^k space-separated integers a_1, a_2, …, a_{2^k} (0 ≤ a_i < 2^k) — the elements of the given array.

Output

If the given array can't be represented as element-wise XOR of two permutations of integers 0, 1, …, 2^k-1, print "Fou".

Otherwise, print "Shi" in the first line.

The next two lines should contain the description of two suitable permutations. The first of these lines should contain 2^k space-separated distinct integers p_{1}, p_{2}, …, p_{2^k}, and the second line should contain 2^k space-separated distinct integers q_{1}, q_{2}, …, q_{2^k}.

All elements of p and q should be between 0 and 2^k - 1, inclusive; p_i ⊕ q_i should be equal to a_i for all i such that 1 ≤ i ≤ 2^k. If there are several possible solutions, you can print any.

Examples

Input


2
0 1 2 3


Output


Shi
2 0 1 3 
2 1 3 0 


Input


2
0 0 0 0


Output


Shi
0 1 2 3 
0 1 2 3 


Input


2
0 1 2 2


Output


Fou

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int N, K, a[(1 << 12)], b[(1 << 12)], p[(1 << 12)], q[(1 << 12)],
    pos[(1 << 12)];
void fix(int i, int j) {
  if ((p[i] ^ q[i]) == b[i]) {
  } else if ((p[i] ^ q[j]) == b[i]) {
    swap(q[i], q[j]);
  } else if ((p[j] ^ q[i]) == b[i]) {
    swap(pos[p[j]], pos[p[i]]);
    swap(p[j], p[i]);
  } else if ((p[j] ^ q[j]) == b[i]) {
    swap(pos[p[j]], pos[p[i]]);
    swap(p[j], p[i]);
    swap(q[i], q[j]);
  } else {
    int t = pos[q[i] ^ b[i]];
    swap(pos[p[t]], pos[p[i]]);
    swap(p[t], p[i]);
    swap(q[t], q[j]);
    fix(t, j);
  }
}
int main() {
  while (cin >> K) {
    int x = 0;
    N = 1 << K;
    for (int i = int(0); i < int(N); i++) {
      cin >> a[i];
      x ^= a[i];
    }
    if (x) {
      cout << "Fou" << endl;
      continue;
    }
    cout << "Shi" << endl;
    for (int i = int(0); i < int(N); i++) {
      b[i] = 0;
      pos[i] = p[i] = q[i] = i;
    }
    for (int i = N - 1; i; i--) {
      b[i - 1] ^= a[i] ^ b[i];
      b[i] = a[i];
      fix(i, i - 1);
      if ((p[i] ^ q[i]) != a[i]) {
        cerr << "ERROR";
      }
    }
    for (int i = int(0); i < int(N); i++) cout << p[i] << " \n"[i == N - 1];
    for (int i = int(0); i < int(N); i++) cout << q[i] << " \n"[i == N - 1];
  }
  return 0;
}