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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?
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.
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.
3135
1 169 196 961 16384 31684 36481 38416 43681
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:
$$$\mathtt{16384}$$$ = $$$\mathtt{128}^2$$$
$$$\mathtt{31684}$$$ = $$$\mathtt{178}^2$$$
$$$\mathtt{36481}$$$ = $$$\mathtt{191}^2$$$
$$$\mathtt{38416}$$$ = $$$\mathtt{196}^2$$$
$$$\mathtt{43681}$$$ = $$$\mathtt{209}^2$$$
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