Madoka and Math Dad

题意翻译

给定正整数 $n$，求最大的数 $k$，使得： - $k$ 的数字和为 $n$。 - $k$ 的每一位都不等于 $0$。 - $k$ 的任意相邻两位都不相同。 多测，$n\le 1000$。

题目描述

Madoka finally found the administrator password for her computer. Her father is a well-known popularizer of mathematics, so the password is the answer to the following problem. Find the maximum decimal number without zeroes and with no equal digits in a row, such that the sum of its digits is $ n $ . Madoka is too tired of math to solve it herself, so help her to solve this problem!

输入输出格式

输入格式

Each test contains multiple test cases. The first line contains a single integer $ t $ ( $ 1 \le t \le 1000 $ ) — the number of test cases. Description of the test cases follows. The only line of each test case contains an integer $ n $ ( $ 1 \le n \le 1000 $ ) — the required sum of the digits.

输出格式

For each test case print the maximum number you can obtain.

输入输出样例

输入样例 #1

5
1
2
3
4
5

输出样例 #1

1
2
21
121
212

说明

The only numbers with the sum of digits equal to $ 2 $ without zeros are $ 2 $ and $ 11 $ . But the last one has two ones in a row, so it's not valid. That's why the answer is $ 2 $ . The only numbers with the sum of digits equal to $ 3 $ without zeros are $ 111 $ , $ 12 $ , $ 21 $ , and $ 3 $ . The first one has $ 2 $ ones in a row, so it's not valid. So the maximum valid number is $ 21 $ . The only numbers with the sum of digits equals to $ 4 $ without zeros are $ 1111 $ , $ 211 $ , $ 121 $ , $ 112 $ , $ 13 $ , $ 31 $ , $ 22 $ , and $ 4 $ . Numbers $ 1111 $ , $ 211 $ , $ 112 $ , $ 22 $ aren't valid, because they have some identical digits in a row. So the maximum valid number is $ 121 $ .