13:I[87,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"Header"] 14:I[1742,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"ProblemView"] 15:T7e5,

Toad 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 $$$a_1, a_2, \ldots, a_{2^k}$$$ ($$$0 \leq a_i \lt 2^k$$$) — 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 "

Xor Permutations

Examples