E. Bet
Tag(s):

## Medium, Prime Factorization

Problem
Editorial
Analytics

King has just won a bet with Saitama (which everyone already knew he would). So as per the rules of the bet Saitama is going to give King $m$ times the amount King bet, where $m$ is the number of factors of the amount King bet. If King had $n$ units of money before the bet then what is the maximum money he can have after the bet?

NOTE: King doesn't have to put all his money in the bet.

Input

First line contains an integer $T$, the number of test cases.

$T$ lines follow, each containing a single integer $n$ - the amount King had before the bet.

Output

Your output should contain $T$ lines, each showing the maximum money that King can have after the bet.

Constraints

$1 \le T \le 10 ^ 5$

$1 \le n \le 10 ^ 6$

SAMPLE INPUT
5
2
4
9
15
50

SAMPLE OUTPUT
4
12
33
75
482

Time Limit: 0,7 sec(s) for each input file.
Memory Limit: 256 MB
Source Limit: 1024 KB
Marking Scheme: Marks are awarded when all the testcases pass.
Allowed Languages: Bash, C, C++, C++14, Clojure, C#, D, Erlang, F#, Go, Groovy, Haskell, Java, Java 8, JavaScript(Rhino), JavaScript(Node.js), Julia, Kotlin, Lisp, Lisp (SBCL), Lua, Objective-C, OCaml, Octave, Pascal, Perl, PHP, Python, Python 3, R(RScript), Racket, Ruby, Rust, Scala, Swift, Swift-4.1, TypeScript, Visual Basic

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