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E. Xor Permutations

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputToad Mikhail has an array of $$$2^k$$$ integers $$$a_1, a_2, \ldots, a_{2^k}$$$.

Find two permutations $$$p$$$ and $$$q$$$ of integers $$$0, 1, \ldots, 2^k-1$$$, such that $$$a_i$$$ is equal to $$$p_i \oplus q_i$$$ for all possible $$$i$$$, or determine there are no such permutations. Here $$$\oplus$$$ denotes the bitwise XOR operation.

Input

The first line contains one integer $$$k$$$ ($$$2 \leq k \leq 12$$$), denoting that the size of the array is $$$2^k$$$.

The next line contains $$$2^k$$$ space-separated integers $$$a_1, a_2, \ldots, a_{2^k}$$$ ($$$0 \leq a_i < 2^k$$$) — the elements of the given array.

Output

If the given array can't be represented as element-wise XOR of two permutations of integers $$$0, 1, \ldots, 2^k-1$$$, 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 $$$p_{1}, p_{2}, \ldots, p_{2^k}$$$, and the second line should contain $$$2^k$$$ space-separated distinct integers $$$q_{1}, q_{2}, \ldots, q_{2^k}$$$.

All elements of $$$p$$$ and $$$q$$$ should be between $$$0$$$ and $$$2^k - 1$$$, inclusive; $$$p_i \oplus q_i$$$ should be equal to $$$a_i$$$ for all $$$i$$$ such that $$$1 \leq i \leq 2^k$$$. 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

Codeforces (c) Copyright 2010-2022 Mike Mirzayanov

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