Compatible Numbers

题意翻译

定义两个整数 $x, y$ 兼容,当且仅当 $x, y$ 在二进制下与的结果为 $0$。 现在给你一个数列 $a_1, a_2, \dots a_n$,对于所有 $i = 1, 2, \dots, n$,求出一个下标 $j$,使得 $a_i$ 与 $a_j$ 兼容。若存在,输出任意一个 $a_j$,否则输出 `-1`。

题目描述

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 $ $ (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.

输入输出格式

输入格式


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.

输出格式


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} $ .

输入输出样例

输入样例 #1

2
90 36

输出样例 #1

36 90

输入样例 #2

4
3 6 3 6

输出样例 #2

-1 -1 -1 -1

输入样例 #3

5
10 6 9 8 2

输出样例 #3

-1 8 2 2 8