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Description

It is interesting to know whether eΠ is larger or smaller than Πe.
Another interesting question is this:
What is the value of x when xΠx?
Obviously x=Π would be one solution.
But are there other solutions?

Formally, given a number a and constraints xa=ax, a>1, x>1,
please find the solutions of x other than x=a.

Input Format

The first line has one integer T, which is the number of test cases.
Each test case are in one line, which contains the number a.
Note that all numbers in the input would have at most four digits after the decimal point.

Output Format

For each test case, please output one line containing the solutions of x, round to four digits after the decimal point.
If there is no solution other than x=a, please output "NO".
If there are more than one solution, please output all of them in increasing order, separated by a white space.

Clarification: If there are two different solutions which become the same after truncation, you have to treat them as different solutions.

Sample Input 1

2
2.0
4.0

Sample Output 1

4.0000
2.0000

Hints

Problem Source

Migrated from old NTUJ.

popo

Subtasks

No. Testdata Range Score

Testdata and Limits

No. Time Limit (ms) Memory Limit (VSS, KiB) Output Limit (KiB) Subtasks
0 4000 65536 200