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 bit = 20;
const int N = 3e5 + 10;
const int mod = 1e9 + 7;
template <typename T>
void read(T &x) {
  char c = getchar();
  int f = 0;
  while (c < '0' || c > '9') f |= (c == '-'), c = getchar();
  for (x = 0; c >= '0' && c <= '9'; c = getchar())
    x = (x << 3) + (x << 1) + (c - '0');
  if (f) x = -x;
}
int k, n, q;
int v[N], p[N], a[N], b[N], pa[N], pb[N];
void fix(int x, int y) {
  int t = pa[v[x] ^ b[x]];
  if (t == x) return;
  if (t == y) {
    swap(pa[a[x]], pa[a[y]]);
    swap(a[x], a[y]);
    return;
  }
  swap(a[t], a[x]);
  swap(pa[a[x]], pa[a[t]]);
  swap(b[y], b[t]);
  swap(pb[b[y]], pb[b[t]]);
  fix(t, y);
}
int main() {
  read(k);
  n = 1 << k;
  for (int i = 0; i < n; ++i) read(p[i]);
  int s = 0;
  for (int i = 0; i < n; ++i) {
    s ^= p[i];
    a[i] = b[i] = pa[i] = pb[i] = i;
  }
  if (s) return 0 * puts("Fou");
  for (int i = 0; i < n - 1; ++i) {
    if (v[i] != p[i]) {
      v[i + 1] ^= v[i] ^ p[i];
      v[i] = p[i];
      fix(i, i + 1);
    }
  }
  puts("Shi");
  for (int i = 0; i < n; ++i) printf("%d ", a[i]);
  puts("");
  for (int i = 0; i < n; ++i) printf("%d ", b[i]);
  puts("");
  return 0;
}