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题目描述

We consider the distance between positive integers in this problem, defined as follows.

A single operation consists in either multiplying a given number by a prime number1 or dividing it by a prime number (if it does divide without a remainder).

The distance between the numbers and , denoted , is the minimum number of operations it takes to transform the number into the number .

For example, .

Observe that the function is indeed a distance function - for any positive integers , and the following hold:

the distance between a number and itself is 0: , the distance from to is the same as from to : , and the triangle inequality holds: .

A sequence of positive integers, , is given.

For each number we have to determine such that and is minimal.

输入格式

In the first line of standard input there is a single integer ().

In the following lines the numbers () are given, one per line.

In tests worth 30% of total point it additionally holds that .

输出格式

Your program should print exactly lines to the standard output, a single integer in each line.

The -th line should give the minimum such that: , and is minimal.

题目大意

题目描述

译自 POI 2012 Stage 1. 「Distance」

定义一次「操作」为将一个正整数除以或乘以一个质数。定义函数 $d(a,b)$ 表示将 $a$ 进行若干次“操作”变成 $b$ 所需要的最小操作次数。例如，$d(69,42)=3$.

$d$ 显然是一个距离函数，满足以下性质：

• $d(a,a) = 0$
• $d(a,b) = d(b,a)$
• $d(a,b) + d(b,c) \ge d(a,c)$

给定 $n$ 个正整数 $a_1, a_2, \ldots, a_n$，对每个 $a_i (1 \le i \le n)$，求 $j$ 使得 $j \neq i$ 且 $d(a_i,a_j)$ 最小。如果有多个满足条件的 $j$，应输出最小的那个。

输入格式

第一行一个正整数 $n (2 \le n \le 100,000)$.

第二行 $n$ 个正整数 $a_1, a_2, \ldots, a_n (1 \le a_i \le 1\ 000\ 000)$.

输出格式

输出 $n$ 行，每行一个整数，表示使 $j \neq i$ 且 $d(a_i,a_j)$ 最小的 $j$.

数据范围

对于 $30\%$ 的数据有 $n \le 1000$.

对于所有数据有 $2 \le n \le 10^5,1 \le a_i \le 10^6$.

翻译来自于 LibreOJ。

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