E. Xor Permutationstime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard 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.InputThe 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.OutputIf 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.ExamplesInput
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

2
0 1 2 3

Shi 2 0 1 3  2 1 3 0  
['constructive algorithms', 'math', '*3100']