Two integers x and y are compatible, if the result of their bitwise "AND" equals zero, that is, a & b = 0. For example, numbers 90 (1011010₂) and 36 (100100₂) are compatible, as 1011010₂ & 100100₂ = 0₂, and numbers 3 (11₂) and 6 (110₂) are not compatible, as 11₂ & 110₂ = 10₂.

You are given an array of integers a₁, a₂, ..., 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 ≤ 10⁶) — the number of elements in the given array. The second line contains n space-separated integers a₁, a₂, ..., a_n (1 ≤ a_i ≤ 4·10⁶) — 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 a₁, a₂, ..., 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 a₁, a₂, ..., a_n.

Compatible Numbers

Examples