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 N = 1 << 12;
int n, m;
int _p[N], _q[N];
int p[N], q[N], a[N], b[N];
void adjust(int i, int j, int x, int& t, int& nx) {
  if ((a[i] ^ x) == (p[j] ^ q[j])) {
    t = -1, nx = 0;
    swap(p[i], p[j]), swap(_p[p[i]], _p[p[j]]);
    swap(q[i], q[j]), swap(_q[q[i]], _q[q[j]]);
    assert((p[i] ^ q[i]) == (a[i] ^ x));
    assert((p[j] ^ q[j]) == (a[j] ^ x));
    a[i] ^= x, a[j] ^= x;
    return;
  }
  if ((a[j] ^ x) == (q[i] ^ p[j])) {
    t = -1, nx = 0;
    swap(q[i], q[j]);
    swap(_q[q[i]], _q[q[j]]);
    assert((p[i] ^ q[i]) == (a[i] ^ x));
    assert((p[j] ^ q[j]) == (a[j] ^ x));
    a[i] ^= x, a[j] ^= x;
    return;
  }
  if ((a[i] ^ x) == (p[j] ^ q[i])) {
    t = -1, nx = 0;
    swap(p[i], p[j]);
    swap(_p[p[i]], _p[p[j]]);
    assert((p[i] ^ q[i]) == (a[i] ^ x));
    assert((p[j] ^ q[j]) == (a[j] ^ x));
    a[i] ^= x, a[j] ^= x;
    return;
  }
  t = _p[q[i] ^ a[i] ^ x];
  nx = p[i] ^ q[j] ^ a[t];
  swap(p[i], p[t]), swap(_p[p[i]], _p[p[t]]);
  swap(q[j], q[t]), swap(_q[q[j]], _q[q[t]]);
  assert((p[i] ^ q[i]) == (a[i] ^ x));
  a[i] ^= x;
  a[j] = p[j] ^ q[j];
  a[t] = p[t] ^ q[t];
}
int main() {
  scanf("%d", &m);
  n = 1 << m;
  for (int i = 0; i < n; i++) {
    p[i] = _p[i] = q[i] = _q[i] = i;
  }
  int sum = 0;
  for (int i = 0; i < n; i++) {
    scanf("%d", b + i);
    sum ^= b[i];
  }
  if (sum) {
    puts("Fou");
    return 0;
  }
  for (int i = 0; i < n - 1; i++) {
    int x = i, y = i + 1, d = a[i] ^ b[i], ny, nd;
    while (d) {
      adjust(x, y, d, ny, nd);
      x = ny;
      d = nd;
    }
  }
  puts("Shi");
  for (int i = 0; i < n; i++) {
    printf("%d ", p[i]);
  }
  putchar('\n');
  for (int i = 0; i < n; i++) {
    printf("%d ", q[i]);
  }
  putchar('\n');
  return 0;
}