Hyper Illuminati

문제

Once again the time dawns to demonstrate the sheer power of the Illuminati. To do so, it was decided to build an n-dimensional hyper-step pyramid using n-dimensional blocks:

• All the steps of the pyramid are n-dimensional hyper-cuboids.
• Every step has a height of exactly 1 block in the n-th dimension.
• The pyramid has s steps and the base step is s blocks long in every other of the n − 1 dimensions.
• Every subsequent higher step is 1 block shorter in each of the n − 1 dimensions than the step below it.
• The top step is exactly 1 block.

To prove their might even further the Illuminati leaders have decided to add two more requirements:

• n must be at least 3.
• The number of blocks used to build the pyramid must be a meaningful number.

Figure H.1: A 3-dimensional hyper pyramid with 3 steps consisting of 14 blocks in total.

입력

The input consists of:

• one line with a single integer m (1 ≤ m ≤ 10¹⁶) . This integer is the meaningful number the leaders have chosen.

출력

If a hyper-step pyramid matching all the requirements exists, output a single line with two integers n and s, the dimension of the pyramid and its number of steps. If none exists, output impossible. If multiple solutions exist, any will be accepted.

14

3 3

9

4 2

24

impossible

9134731356568978

5 2147