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E. Compatible Numbers

time limit per test

4 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputTwo integers *x* and *y* are compatible, if the result of their bitwise "AND" equals zero, that is, *a* & *b* = 0. For example, numbers 90 (1011010_{2}) and 36 (100100_{2}) are compatible, as 1011010_{2} & 100100_{2} = 0_{2}, and numbers 3 (11_{2}) and 6 (110_{2}) are not compatible, as 11_{2} & 110_{2} = 10_{2}.

You are given an array of integers *a*_{1}, *a*_{2}, ..., *a*_{n}. Your task is to find the following for each array element: is this element compatible with some other element from the given array? If the answer to this question is positive, then you also should find any suitable element.

Input

The first line contains an integer *n* (1 ≤ *n* ≤ 10^{6}) — the number of elements in the given array. The second line contains *n* space-separated integers *a*_{1}, *a*_{2}, ..., *a*_{n} (1 ≤ *a*_{i} ≤ 4·10^{6}) — the elements of the given array. The numbers in the array can coincide.

Output

Print *n* integers *ans*_{i}. If *a*_{i} isn't compatible with any other element of the given array *a*_{1}, *a*_{2}, ..., *a*_{n}, then *ans*_{i} should be equal to -1. Otherwise *ans*_{i} is any such number, that *a*_{i} & *ans*_{i} = 0, and also *ans*_{i} occurs in the array *a*_{1}, *a*_{2}, ..., *a*_{n}.

Examples

Input

2

90 36

Output

36 90

Input

4

3 6 3 6

Output

-1 -1 -1 -1

Input

5

10 6 9 8 2

Output

-1 8 2 2 8

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

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