Problem F: Summer camp

## Problem F: Summer camp

Time Limit: 1 Sec  Memory Limit: 128 MB
Submit: 1350  Solved: 239
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## Description

This summer holiday, members in SUSTechCPC went to Qinhuangdao to participate in a summer camp there. As they enjoyed a lot, they decided to take a group photo.

There are $$n$$ member(s) in SUSTechCPC, and they want to stand in $$k(k\ge2)$$ rows because it is too crowded to stand in only one row. To make the photo more beautiful, the number of people standing in the $$i^{th}$$ row should be exactly one more than the number of people standing in the $$(i-1)^{th}$$ row. Since they do not want to stand in too many rows, please tell them the minimum possible number of rows $$k$$ or determine that it is impossible to find any valid arrangement.

## Input

The first line of the input contains one integer $$T$$, indicates the number of testcases.

For each testcase, there is only one line contains one integer $$n(1\le n \le 1\ 000\ 000\ 000)$$.

## Output

Print one single integer, the minimum possible $$k$$ described above.

If there is no such $$k$$, please output 'impossible' (without quotes).

## Sample Input

3
8
10
24

## Sample Output

impossible
4
3


## HINT

10 = 1 + 2 + 3 + 4

24 = 7 + 8 + 9

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