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;
const int c = 5002;
int n, a[c], b[c], ia[c], t[c], res[c], xo;
void valt(int p1, int p2) {
  if (p1 == p2) return;
  int p3 = ia[t[p1] ^ b[p1]];
  swap(ia[a[p1]], ia[a[p3]]), swap(a[p1], a[p3]);
  swap(b[p2], b[p3]);
  valt(p3, p2);
}
int main() {
  ios_base::sync_with_stdio(false);
  cin >> n, n = (1 << n);
  for (int i = 0; i < n; i++) {
    cin >> res[i], xo ^= res[i];
    a[i] = i, b[i] = i, ia[i] = i;
  }
  if (xo) {
    cout << "Fou\n";
    return 0;
  }
  cout << "Shi\n";
  for (int i = 0; i < n - 1; i++) {
    xo = t[i] ^ res[i];
    t[i] ^= xo, t[i + 1] ^= xo;
    valt(i, i + 1);
  }
  for (int i = 0; i < n; i++) cout << a[i] << " ";
  cout << "\n";
  for (int i = 0; i < n; i++) cout << b[i] << " ";
  cout << "\n";
  return 0;
}