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;
inline void open(const char *s) {}
inline int rd() {
  static int x, f;
  x = 0;
  f = 1;
  char ch = getchar();
  for (; ch < '0' || ch > '9'; ch = getchar())
    if (ch == '-') f = -1;
  for (; ch >= '0' && ch <= '9'; ch = getchar()) x = x * 10 + ch - '0';
  return f > 0 ? x : -x;
}
const int N = 1 << 12;
int n, pos[N], a[N], b[N];
int p[N], q[N];
void fix(int x, int y) {
  while (1) {
    int t = pos[q[x] ^ a[x]];
    if (t == x)
      return;
    else if (t == y) {
      swap(p[x], p[y]);
      swap(pos[p[x]], pos[p[y]]);
      return;
    }
    swap(q[y], q[t]);
    swap(p[x], p[y]);
    swap(pos[p[x]], pos[p[y]]);
    swap(p[x], p[t]);
    swap(pos[p[x]], pos[p[t]]);
    x = t;
  }
}
int main() {
  n = rd();
  int s = 0;
  for (int i = 0; i <= (1 << n) - 1; i++) {
    b[i] = rd();
    s ^= b[i];
  }
  if (s) return puts("Fou"), 0;
  for (int i = 0; i <= (1 << n) - 1; i++) p[i] = q[i] = pos[i] = i;
  for (int i = 0; i <= (1 << n) - 1; i++) {
    a[i + 1] ^= (a[i] ^ b[i]);
    a[i] = b[i];
    fix(i, i + 1);
  }
  puts("Shi");
  for (int i = 0; i <= (1 << n) - 1; i++) cout << p[i] << ' ';
  cout << '\n';
  for (int i = 0; i <= (1 << n) - 1; i++) cout << q[i] << ' ';
  cout << '\n';
  return 0;
}