Codeforces Round 690 (Div. 3) |
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Finished |

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brute force

greedy

math

*900

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C. Unique Number

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou are given a positive number $$$x$$$. Find the smallest positive integer number that has the sum of digits equal to $$$x$$$ and all digits are distinct (unique).

Input

The first line contains a single positive integer $$$t$$$ ($$$1 \le t \le 50$$$) — the number of test cases in the test. Then $$$t$$$ test cases follow.

Each test case consists of a single integer number $$$x$$$ ($$$1 \le x \le 50$$$).

Output

Output $$$t$$$ answers to the test cases:

- if a positive integer number with the sum of digits equal to $$$x$$$ and all digits are different exists, print the smallest such number;
- otherwise print -1.

Example

Input

4 1 5 15 50

Output

1 5 69 -1

Codeforces (c) Copyright 2010-2024 Mike Mirzayanov

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