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 <typename T>
inline T read(register T& t) {
  register T f = 1;
  register char ch = getchar();
  t = 0;
  while (ch < '0' || ch > '9') {
    if (ch == '-') f = -f;
    ch = getchar();
  }
  while (ch >= '0' && ch <= '9') t = t * 10 + ch - '0', ch = getchar();
  t *= f;
  return t;
}
template <typename T, typename... Args>
inline void read(T& t, Args&... args) {
  read(t);
  read(args...);
}
int k, n;
int a[10005];
int p[10005], q[10005], v[10005], bel[10005];
void fix(int i, int j) {
  int d = q[i] ^ v[i], tp = bel[d];
  if (tp == i) return;
  if (tp == j) return swap(p[i], p[j]), swap(bel[p[i]], bel[p[j]]), void();
  swap(bel[p[i]], bel[p[tp]]);
  swap(p[i], p[tp]);
  swap(q[tp], q[j]);
  fix(tp, j);
}
int main() {
  read(k);
  n = 1 << k;
  int qwq = 0;
  for (int i = 0; i < n; i++)
    read(a[i]), p[i] = q[i] = i, bel[i] = i, qwq ^= a[i];
  if (qwq) return printf("Fou\n"), 0;
  for (int i = 0; i < n - 1; i++) {
    int d = a[i] ^ v[i];
    if (d == 0) continue;
    v[i] ^= d;
    v[i + 1] ^= d;
    fix(i, i + 1);
  }
  printf("Shi\n");
  for (int i = 0; i < n; i++) printf("%d ", p[i]);
  printf("\n");
  for (int i = 0; i < n; i++) printf("%d ", q[i]);
  printf("\n");
}