CF599D.Spongebob and Squares

普及/提高-

通过率：0%

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题目描述

Spongebob is already tired trying to reason his weird actions and calculations, so he simply asked you to find all pairs of n and m, such that there are exactly $x$ distinct squares in the table consisting of $n$ rows and $m$ columns. For example, in a $3×5$ table there are $15$ squares with side one, $8$ squares with side two and $3$ squares with side three. The total number of distinct squares in a $3×5$ table is $15+8+3=26$ .

输入格式

The first line of the input contains a single integer $x$ ( $1<=x<=10^{18}$ ) — the number of squares inside the tables Spongebob is interested in.

输出格式

First print a single integer $k$ — the number of tables with exactly $x$ distinct squares inside.

Then print $k$ pairs of integers describing the tables. Print the pairs in the order of increasing $n$ , and in case of equality — in the order of increasing $m$ .

输入输出样例

输入#1
```
26
```
输出#1
```
6
1 26
2 9
3 5
5 3
9 2
26 1
```
输入#2
```
2
```
输出#2
```
2
1 2
2 1
```
输入#3
```
8
```
输出#3
```
4
1 8
2 3
3 2
8 1
```

说明/提示

In a $1×2$ table there are $2$ $1×1$ squares. So, $2$ distinct squares in total.

In a $2×3$ table there are $6$ $1×1$ squares and $2$ $2×2$ squares. That is equal to $8$ squares in total.

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