digits-1

We call two (positive) numbers friends if the sum of their digits is equal. For example, the following numbers are all friends with each other:
3,12,21,30,102,111,120,201,210
Considering, for instance, 111: among numbers smaller than it, its closest friend is 102; among numbers larger than it, the closest friend is 120. We want to determine these closest friends for various numbers. That is: given $X$, find the largest possible $L$ and smallest possible $R$ such that $0 < L < X < R$, and both $L$ and $R$ have the same digit sum as $X$.

Input specification

The first line contains a single integer $T$: the number of test cases. Then $T$ lines follow, each containing a number $X$.

Output specification

Output $T$ lines, each containing the requested $L$ and $R$ numbers. If for a given $X$ there is no $L$ or $R$, output $−1$ in the corresponding position.

Constraints

$1\le T \le 100$
$1\le X \le 1\_000\_000\_000\_000\_000$

Sample input 1

1. 5
2. 10
3. 2
4. 738374
5. 123123123
6. 11000

Sample output 1

1. 1 100
2. -1 11
3. 738365 738383
4. 123123114 123123132
5. 10100 20000