Problems

Status

Rank

Problem 1109
Beer Refrigerator
Time Limit: 1000ms
Memory Limit: 65536kb
Description
Beer Lovers Club makes regular parties. They hate warm beer, but club’s refrigerator is too small to store enough beer for the whole company. So they decided to order a special super-big beer refrigerator. The new refrigerator should be a parallelepiped a*b*c and store exactly n cubical 1*1*1 beer boxes (the club has n members). To decrease losses of cold, the total area of the surface of the refrigerator must be as small as possible.
For example, if the capacity of the refrigerator must be 12, the possible variants are:
DimensionsSurface Area
3*2*232
4*3*138
6*2*140
12*1*150

The best variant in this case is 3*2*2.
Help the beer lovers to find the optimal dimensions for their new refrigerator.
Input
Each case contains single integer number n (1 <= n <= 106) — the capacity of the refrigerator. Process to the end of file.
Output
Output three integer numbers: a, b and c — the optimal dimensions of the refrigerator. (a<=b<=c)
Sample Input
```12
13
1000000```
Sample Output
```2 2 3
1 1 13
100 100 100```
University of Science and Technology of China
Online Judge for ACM/ICPC
Processed in 1.6ms with 1 query(s).