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;
int a[5555], b[5555], c[5555];
int pos[5555];
int main() {
  cin >> n;
  n = (1 << n);
  int tot = 0;
  for (int i = 0; i < n; i++) scanf("%d", c + i), tot ^= c[i];
  if (tot) return puts("Fou"), 0;
  puts("Shi");
  for (int i = 0; i < n; i++) a[i] = b[i] = pos[i] = i;
  for (int i = 0; i < n; i++) {
    int u = i;
    while ((a[u] ^ b[u]) != c[u]) {
      int v = pos[c[u] ^ b[u]];
      swap(a[u], a[v]);
      swap(pos[a[u]], pos[a[v]]);
      if (v > i) break;
      swap(b[v], b[i + 1]);
      u = v;
    }
  }
  for (int i = 0; i < n; i++) printf("%d ", a[i]);
  for (int i = 0; i < n; i++) printf("%d ", b[i]);
  return 0;
}