Mathematical Problem
题意翻译
给定奇数 $n$,求出 $n$ 个正整数满足:
- 都是完全平方数。
- 长度为 $n$ 且没有前导 $0$。
- 组成这 $n$ 个数的数字($[0,9]$ 内数字)组成的**可重集**相同。
输出任意一种方案。
题目描述
The mathematicians of the 31st lyceum were given the following task:
You are given an odd number $ n $ , and you need to find $ n $ different numbers that are squares of integers. But it's not that simple. Each number should have a length of $ n $ (and should not have leading zeros), and the multiset of digits of all the numbers should be the same. For example, for $ \mathtt{234} $ and $ \mathtt{432} $ , and $ \mathtt{11223} $ and $ \mathtt{32211} $ , the multisets of digits are the same, but for $ \mathtt{123} $ and $ \mathtt{112233} $ , they are not.
The mathematicians couldn't solve this problem. Can you?
输入输出格式
输入格式
The first line contains an integer $ t $ ( $ 1 \leq t \leq 100 $ ) — the number of test cases.
The following $ t $ lines contain one odd integer $ n $ ( $ 1 \leq n \leq 99 $ ) — the number of numbers to be found and their length.
It is guaranteed that the solution exists within the given constraints.
It is guaranteed that the sum of $ n^2 $ does not exceed $ 10^5 $ .
The numbers can be output in any order.
输出格式
For each test case, you need to output $ n $ numbers of length $ n $ — the answer to the problem.
If there are several answers, print any of them.
输入输出样例
输入样例 #1
3
1
3
5
输出样例 #1
1
169
196
961
16384
31684
36481
38416
43681
说明
Below are the squares of the numbers that are the answers for the second test case:
$ \mathtt{169} $ = $ \mathtt{13}^2 $
$ \mathtt{196} $ = $ \mathtt{14}^2 $
$ \mathtt{961} $ = $ \mathtt{31}^2 $
Below are the squares of the numbers that are the answers for the third test case:
$ \mathtt{16384} $ = $ \mathtt{128}^2 $
$ \mathtt{31684} $ = $ \mathtt{178}^2 $
$ \mathtt{36481} $ = $ \mathtt{191}^2 $
$ \mathtt{38416} $ = $ \mathtt{196}^2 $
$ \mathtt{43681} $ = $ \mathtt{209}^2 $