JMU CS280 SP18 WK10

Start

2018-03-20 20:30 CET

JMU CS280 SP18 WK10

End

2018-03-24 04:59 CET
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Problem B
The Owl and the Fox

Fox Mithra has finally learned the numbers and he is now familiar with the concept of ‘one’, ’two’, ‘three’ and also even ‘zero’, ‘minus one’, ‘minus two’ and so on. Really, an achievement for such a small fox. He took the textbook and copied the integers from the book one by one from the smallest to the biggest on the wall of his enclosure in the ZOO.

“Look, there is something wrong with your sequence on the wall”, said the owl who just landed on the branch above Mithra’s head. “You should put $30$ between $20$ and $22$, there.”

“Why?”

“Because the importance of a number is judged by the sum of its digits. $30$ is therefore less important than $22$ and it is more important than $20$. And obviously, $30$ should be equally close to $20$ and $22$ because its sum of digits differs only by one from both $20$ and $22$.”

“I see,” replied Mithra, “you are really clever. Can you help me please to rearrange the sequence correctly? Each time I tell you a number $N$ you will tell me the closest smaller number with sum of digits less by one than the sum of digits of $N$.”

“With pleasure,” nodded the owl majestically.

Your task is to imitate the owl’s task. Given an integer $N$ you have to find the biggest integer which is smaller than $N$ with sum of digits less by one than the sum of digits of $N$.

Input

The first line of input contains the number of test cases $T$ ($1 \leq T \leq 100\, 000$). The descriptions of the test cases follow:

Each case consists of a line containing a single integer $N$ ($1 \leq N \leq 100\, 000$).

Output

For each test case print on a separate line the number demanded by fox Mithra.

Sample Input 1 Sample Output 1
4
30
199
1000
1520
20
198
0
1510