Product of Two Numbers 2

Time limit2sMemory limit512 MB

Summary

Given a, b, c, choose positive A, B, C with A*B=C minimizing |A-a|+|B-b|+|C-c|.

Level: Hard8 of 10
Topics: Math, Number theory, Brute force
Solved: No attempts yet

Problem

You are given positive integers $a$ , $b$ , and $c$ . Among all positive integers $A$ , $B$ , and $C$ with $A \times B = C$ , find the smallest possible value of $|A - a| + |B - b| + |C - c|$ .

$|x|$ is the absolute value of $x$ .

Input

The first line contains $a$ , $b$ , and $c$ , separated by spaces. ( $1 \le a, b, c \le 10^9$ )

Output

Print the minimum value of $|A - a| + |B - b| + |C - c|$ on the first line. $A$ , $B$ , and $C$ must all be positive integers with $A \times B = C$ .

Examples4

Example 1
Input
```
19 28 522
```
Expected output
```
2
```
Example 2
Input
```
10 30 500
```
Expected output
```
11
```
Example 3
Input
```
111 111 12321
```
Expected output
```
0
```
Example 4
Input
```
1000 100 10
```
Expected output
```
1089
```