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 JAVA):

Solution:
import java.io.*;
import java.util.*;

public class CF1168E {
	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int k = Integer.parseInt(br.readLine());
		StringTokenizer st = new StringTokenizer(br.readLine());
		int n = 1 << k;

		int[] a = new int[n];
		int checkXOR = 0;

		for (int i = 0; i < n; i++)
		{
			a[i] = Integer.parseInt(st.nextToken());
			checkXOR = checkXOR^a[i];
		}

		if (checkXOR != 0) 
		{
			System.out.println("Fou");
			return;
		}

		int[] p = new int[n];
		int[] q = new int[n];
		int[] indexQ = new int[n];

		for (int i = 0; i < n; i++) p[i] = q[i] = indexQ[i] = i;

		for (int i = 0; i < n - 1; i++)
		{
			for (int u = i, v; u <= i && (a[u] ^ p[u] ^ q[u]) != 0; u = v) 
			{
				v = indexQ[a[u] ^ p[u]];
				int temp;
				temp = q[u]; q[u] = q[v]; q[v] = temp;
				temp = indexQ[q[u]]; indexQ[q[u]] = indexQ[q[v]]; indexQ[q[v]] = temp;
				temp = p[v]; p[v] = p[n - 1]; p[n - 1] = temp;
			}
		}
		
		System.out.println("Shi");

		for (int i = 0; i < n; i++) System.out.print(p[i] + " ");
		System.out.println();
		for (int i = 0; i < n; i++) System.out.print(q[i] + " ");
		System.out.println();
	}
}