Perfect Number Finder

You are given an integer N. Your task is to find and output the smallest perfect number that is strictly greater than N. A perfect number is a positive integer which is equal to the sum of its proper divisors (excluding itself). In other words, a number \(n\) is perfect if

\(\sum_{d|n,\ d<n} d = n\)

If no such perfect number exists under the constraint described below, output "Not found".

Note: For this problem, if N is greater than or equal to \(10^{18}\), you should output "Not found" immediately.

inputFormat

The input is given via standard input (stdin). The first line contains a single integer T denoting the number of test cases. Each of the next T lines contains one integer N.

outputFormat

For each test case, output a single line on standard output (stdout) containing the smallest perfect number greater than N. If there is no such perfect number under the constraints, output "Not found".## sample

3
5
28
1000000000000000000

6
496
Not found