409023: GYM103416 C Mura and love

Mura is a tree-lover. Unfortunately, recently, he has lost his favorite rooted tree $$$t$$$ of size $$$n$$$, each node $$$v$$$ of which was assigned a value ($$$v.val$$$).

$$$t$$$ satisfies the following:

1. The next pseudocode function returns a given array $$$a$$$ of size $$$n$$$ as a result, if $$$t$$$ is passed as an argument:

   
   Array to_array(Tree t):
       Array res = [t.root.val]
       
       for each child v of t.root:
           res = res + to_array(v.subtree)
   
       return res
   

2. Among all trees that satisfy the first condition, $$$t$$$ has the maximum sum of $$$f(v)$$$ over all nodes $$$v$$$ of the tree. Here, $$$f(v) = xor(v) \curlywedge size(v)$$$, where:
   • $$$xor(v)$$$ — the result of bitwise XOR operation over the values of all nodes in the subtree of $$$v$$$.
   • $$$size(v)$$$ — the number of nodes in the subtree of $$$v$$$.
   • $$$\curlywedge$$$ — bitwise AND operation.

Mura knows, that he will never see his favorite tree again. But, at least, he wants to find the value of the sum of $$$f(v)$$$ over all nodes $$$v$$$ of $$$t$$$. Can you help him?

The first line contains an integer $$$n$$$ ($$$1 \leq n \leq 1000$$$) — the size of the tree $$$t$$$ and the array $$$a$$$.

The second line contains $$$n$$$ integers $$$a_1, a_2,...a_{n - 1}, a_{n}$$$ ($$$0 \leq a_i \leq 10^6$$$) — the array $$$a$$$.

Output the sum of $$$f(v)$$$ over all nodes $$$v$$$ of $$$t$$$.

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