###### Category

###### Similar Problems

## 0770. Beer Refrigerator

###### Time limit : 1000 ms

Memory limit : 64 mb

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

2 × 2 × 3 32

1 × 3 × 4 38

1 × 2 × 6 40

1 × 1 × 12 50

The best variant in this case is 2 × 2 × 3.

Help the beer lovers to find the optimal dimensions for their new refrigerator.

Input

The input file contains single
integer number n (1 ≤ n ≤ 10^{6}) — the capacity of the
refrigerator.

Output

Output three
integer numbers: *a*, *b* and *c*(1≤*a≤b≤c*) — the optimal dimensions of the refrigerator. If there are several solutions output with smallest *a*.

Samples

№ |
Input |
Output |

1 |
12 |
2 2 3 |

2 |
13 |
1 1 13 |

3 |
1000000 |
100 100 100 |

Text from: Uzbekistan subregional