Beer Refrigerator
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:
| Dimensions | Surface Area | |
| 3 × 2 × 2 | 32 | |
| 4 × 3 × 1 | 38 | |
| 6 × 2 × 1 | 40 | |
| 12 × 1 × 1 | 50 |
The best variant in this case is 3 × 2 × 2.
Help the beer lovers to find the optimal dimensions of their new refrigerator.
Input
The input file contains single integer number n (1 ≤ n ≤ 106) — the capacity of the refrigerator. Help the beer lovers to find the optimal dimensions of their new refrigerator.
Output
Output three integer numbers: a, b and c — the optimal dimensions of the refrigerator. If there are several solutions, output any of them.
#1 12 #2 13 #3 1000000
#1 3 2 2 #2 1 13 1 #3 100 100 100
Source
Northeastern Europe 2007, Northern Subregion