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>
const int MAXN = 1 << 12;
int A[MAXN], B[MAXN], now[MAXN], tar[MAXN], n, to[MAXN];
void fit(int i, int j) {
  if (A[i] == (B[i] ^ now[i])) return;
  int t = to[A[i] ^ now[i]];
  if (t == j) return std::swap(B[i], B[t]), std::swap(to[B[i]], to[B[j]]);
  std::swap(B[i], B[t]);
  std::swap(to[B[i]], to[B[t]]);
  std::swap(A[j], A[t]);
  fit(t, j);
}
int main() {
  scanf("%d", &n);
  n = 1 << n;
  int t = 0;
  for (int i = 0; i != n; ++i) {
    scanf("%d", tar + i);
    to[i] = A[i] = B[i] = i;
    t ^= tar[i];
  }
  if (t) return puts("Fou"), 0;
  for (int i = 0; i < n - 1; ++i) {
    now[i + 1] ^= now[i] ^ tar[i];
    now[i] = tar[i];
    fit(i, i + 1);
  }
  puts("Shi");
  for (int i = 0; i != n; ++i) printf("%d ", A[i]);
  putchar(10);
  for (int i = 0; i != n; ++i) printf("%d ", B[i]);
  putchar(10);
  return 0;
}