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770. Beer Refrigerator
Vaqt limiti: 1 sekund
Xotira limiti: 64 MB

Beer Lovers Club makes regular parties. They hate warm beer, but clubs 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 ≤ 106) 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

 

Tayyorladi: Azat Yusupov
Text from: Uzbekistan subregional
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