5014: Spongebob and Squares
内存限制：256 MB
时间限制：2 S
标准输入输出
题目类型：传统
评测方式：文本比较
上传者：
提交：3
通过：3
题目描述
D. Spongebob and Squares
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output 海绵宝宝已经厌倦了解释他奇怪的行为和计算，所以他只要求你找到所有n和m对，这样在由n行和m列组成的表中就有x个不同的正方形。例如，在一张3×5的桌子上，有15个正方形边长为1，8个正方形边长为2，3个正方形边长为3。3×5表格中不同方块的总数为15+8+3=26。
输入
输入的第一行包含一个整数x（1≤x≤1018），即Spongebob感兴趣的表格中的正方形数量。
输出
首先打印一个整数k–表的数量，其中正好有x个不同的正方形。
然后打印描述表格的k对整数。按增加n的顺序打印对，如果相等，则按增加m的顺序打印。
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.
Input
The first line of the input contains a single integer x (1≤x≤1018)− the number of squares inside the tables Spongebob is interested in.
Output
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.
Examples
Input
26
Output
6 1 26 2 9 3 5 5 3 9 2 26 1
Input
2
Output
2 1 2 2 1
Input
8
Output
4 1 8 2 3 3 2 8 1
Note
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. 
输入格式
输出格式
输入样例 复制
输出样例 复制