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 N = 4096;
int k, n, a[N], b[N], sum, p[N], ip[N], q[N];
void maintain(int i, int j) {
  int x = p[i] ^ q[i] ^ b[i], t = ip[p[i] ^ x];
  if (!x) return;
  std::swap(p[i], p[t]);
  std::swap(q[t], q[j]);
  std::swap(ip[p[i]], ip[p[t]]);
  maintain(t, j);
}
int main() {
  std::ios::sync_with_stdio(0), std::cin.tie(0);
  std::cin >> k, n = 1 << k;
  for (int i = 0; i < n; ++i) std::cin >> a[i], sum ^= a[i];
  if (sum) return std::cout << "Fou\n", 0;
  std::cout << "Shi\n";
  for (int i = 0; i < n; ++i) p[i] = ip[i] = q[i] = i;
  for (int i = 0; i < n - 1; ++i)
    b[i + 1] ^= b[i] ^ a[i], b[i] = a[i], maintain(i, i + 1);
  for (int i = 0; i < n; ++i) std::cout << p[i] << ' ';
  std::cout << '\n';
  for (int i = 0; i < n; ++i) std::cout << q[i] << ' ';
  std::cout << '\n';
  return 0;
}