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;
int gi() {
  char cc = getchar();
  int cn = 0, flus = 1;
  while (cc < '0' || cc > '9') {
    if (cc == '-') flus = -flus;
    cc = getchar();
  }
  while (cc >= '0' && cc <= '9') cn = cn * 10 + cc - '0', cc = getchar();
  return cn * flus;
}
const int N = (1 << 12) + 5;
int k, n, a[N], v[N], p[N], q[N], Id[N];
void fix(int x, int y) {
  int u = q[x] ^ v[x];
  if (Id[u] == x) return;
  if (Id[u] == y) {
    swap(p[x], p[y]), swap(Id[p[x]], Id[p[y]]);
    return;
  }
  int k = Id[u];
  swap(p[x], p[k]), swap(Id[p[x]], Id[p[k]]), swap(q[k], q[y]);
  fix(k, y);
}
signed main() {
  k = gi(), n = (1 << k);
  int t = 0;
  for (register int i = (0); i < (n); ++i) a[i] = gi(), t ^= a[i];
  for (register int i = (0); i < (n); ++i) p[i] = q[i] = Id[i] = i;
  if (t) {
    puts("Fou");
    exit(0);
  }
  for (register int i = (0); i < (n - 1); ++i) {
    if (a[i] != v[i]) v[i + 1] ^= (a[i] ^ v[i]), v[i] = a[i], fix(i, i + 1);
  }
  puts("Shi");
  for (register int i = (0); i < (n); ++i) printf("%d ", p[i]);
  puts("");
  for (register int i = (0); i < (n); ++i) printf("%d ", q[i]);
  return 0;
}