G. Getting the Real Weight
time limit per test
0.5 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

John tries his best to stay fit. This is why he measures everything he eats, every calorie he burns doing exercise, and his weight every single morning.

The old scale that John uses to track his weight every morning broke last night, John rushed to the supermarket and bought the first scale he found. After returning to home put batteries on the scale, and tested it. What a surprise! He seems to be heavier in this scale than what he weighted in the previous one, thinking it was just the rush of lossing his weight track, he went to sleep. This morning John tested the scale again and he is now $$$X$$$ grams heavier than last night, before returning the scale to the supermarket John took the user manual and read carefull a note: "The weight shown in the scale is the square of the real weight".

Given the value $$$X$$$, find all possible real John weights after the morning weighting, sorted in ascending order. You can assume all weights are positive integers.

Input

The first and only line of input contains a single integer $$$X$$$ ($$$1 \leq X \leq 10^5$$$) ,representing, the amount of grams John is heavier this morning compared to last night weighting

Output

Output two lines, the first line should contain a number $$$P$$$, representing the number of possible real John weights. The second and last line should contain $$$P$$$ integer numbers separated by a space, representing each of the possible real weights. This list should be in ascending order. The second line should be printed only if there are elements in the list.

Examples
Input
15
Output
2
4 8
Input
16
Output
1
5
Note

In the first case there are two possible real weights: $$$4$$$, and $$$8$$$. Since John weights $$$15$$$ grams more than last night, it could be that on the night the real weight of John was $$$1$$$, the scale showed $$$1^2 = 1$$$ and today he sees $$$4^2 = 16$$$ which is $$$X = 15$$$ grams more than last night so he went from $$$1$$$ to $$$4$$$. On the other side he could go from $$$7$$$ to $$$8$$$.