Problem A - Rectangles

The problem concerns arranging a number of unit squares into different rectangles modulo rotation. For example, with 6 unit squares one can form 2 different rectangles: 1x6 and 2x3.

Your task is to write a program which for a given integer n, 0 < n, outputs the minimal number of unit squares that can be arranged into exactly n rectangles.

Input consists of a sequence of positive integers separated by whitespace. For each input integer n your program should output either

Sample input

1 4 19 48 71

Output for sample input

1
24
786432
27720
Too big