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 N = 10005;
int a[N], b[N], p[N], q[N], pos[N];
int n, m, S;
void work(int x, int y) {
  for (;;) {
    int z = pos[q[x] ^ b[x]];
    if (z == x) return;
    if (z == y) {
      swap(p[x], p[y]);
      swap(pos[p[x]], pos[p[y]]);
      return;
    }
    swap(q[y], q[z]);
    swap(p[x], p[y]);
    swap(pos[p[x]], pos[p[y]]);
    swap(p[x], p[z]);
    swap(pos[p[x]], pos[p[z]]);
    x = z;
  }
}
int main() {
  scanf("%d", &n);
  m = (1 << n) - 1;
  for (int i = (int)(0); i <= (int)(m); i++) scanf("%d", &a[i]), S ^= a[i];
  if (S) return puts("Fou"), 0;
  for (int i = (int)(0); i <= (int)(m); i++) p[i] = q[i] = pos[i] = i;
  for (int i = (int)(0); i <= (int)(m - 1); i++) {
    b[i + 1] = b[i] ^ a[i];
    b[i] = a[i];
    work(i, i + 1);
  }
  puts("Shi");
  for (int i = (int)(0); i <= (int)(m); i++) printf("%d ", p[i]);
  puts("");
  for (int i = (int)(0); i <= (int)(m); i++) printf("%d ", q[i]);
}