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;
template <class T1, class T2>
inline void chkmin(T1 &x, const T2 &y) {
  if (x > y) x = y;
}
template <class T1, class T2>
inline void chkmax(T1 &x, const T2 &y) {
  if (x < y) x = y;
}
const int MAXN = 4100;
int k;
int a[MAXN];
int n;
int b[MAXN];
int p[MAXN], q[MAXN];
int id[MAXN];
void change(int i, int j) {
  if (q[i] == (p[i] ^ b[i])) {
    return;
  }
  if (q[i] == (p[i] ^ b[j])) {
    swap(id[p[i]], id[p[j]]);
    swap(p[i], p[j]);
    swap(q[i], q[j]);
    return;
  }
  if (q[i] == (p[j] ^ b[i])) {
    swap(id[p[i]], id[p[j]]);
    swap(p[i], p[j]);
    return;
  }
  if (q[i] == (p[j] ^ b[j])) {
    swap(q[i], q[j]);
    return;
  }
  int t = id[b[i] ^ q[i]];
  swap(id[p[t]], id[p[i]]);
  swap(q[t], q[i]);
  swap(q[t], q[j]);
  swap(q[i], q[j]);
  swap(p[t], p[i]);
  change(t, j);
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  cin >> k;
  n = (1 << k);
  int cur = 0;
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    cur ^= a[i];
  }
  if (cur) {
    cout << "Fou\n";
    return 0;
  }
  cout << "Shi\n";
  for (int i = 0; i < n; i++) {
    p[i] = i;
    q[i] = i;
    id[i] = i;
  }
  for (int i = 0; i < n - 1; i++) {
    b[i + 1] ^= (a[i] ^ b[i]);
    b[i] = a[i];
    change(i, i + 1);
  }
  for (int i = 0; i < n; i++) {
    cout << p[i] << ' ';
  }
  cout << '\n';
  for (int i = 0; i < n; i++) {
    cout << q[i] << ' ';
  }
  cout << '\n';
}