About the Sprite#2893

About the Sprite

0.5 seconds

256 megabytes

Easy

The 8th grade class decided to bring a lot of Sprite to their gathering. To do this, they are planning to build a portable cooler with dimensions $a \times b \times c$ a \times b \times c, which will fit exactly $n$ cubic cans of Sprite, each of size $1 \times 1 \times 1$ 1 \times 1 \times 1. To keep the lemonade as cold as possible, they want to minimize heat loss, i.e., minimize the surface area of the cooler.

For example, if the cooler needs to have capacity $12$ , the following options are possible:

$3 \times 2 \times 2 \to 32$ 3 \times 2 \times 2 \to 32
$4 \times 3 \times 1 \to 38$ 4 \times 3 \times 1 \to 38
$6 \times 2 \times 1 \to 40$ 6 \times 2 \times 1 \to 40
$12 \times 1 \times 1 \to 50$ 12 \times 1 \times 1 \to 50

In this case, the optimal cooler is $3 \times 2 \times 2$ 3 \times 2 \times 2.

Help the 8th grade class find the optimal cooler for any given $n$ .

Input

A single integer $n$ ( $1 \leq n \leq 1 0^{6}$ 1 \le n \le 10^6).

Output

Three integers $a$ , $b$ , $c$ ( $1 \leq a, b, c \leq 1 0^{6}$ 1 \le a, b, c \le 10^6) — the dimensions of the best cooler.

Print the numbers in non-decreasing order.

Examples

Example 1

Loading

a \times b \times c

1 \times 1 \times 1

3 \times 2 \times 2 \to 32

4 \times 3 \times 1 \to 38

6 \times 2 \times 1 \to 40

12 \times 1 \times 1 \to 50

3 \times 2 \times 2

1 \leq n \leq 1 0^{6}

1 \leq a, b, c \leq 1 0^{6}