Problem Statement

Given an integer $N$, output all continuous positive integer sequences with a sum of $N$ and a length greater than or equal $2$ in order.

Constraints

• $1\leq N\leq 10^{16}$.
• $N$ is a positive integer.

Subscores

• $100$ points will be awarded for passing the test set satisfying $N\leq10^6$.

Input

Input is given from Standard Input in the following format:

$\color{#cccccc}\boxed{\color{white}{\large{|}}\color{black}N\color{white}{\large{|}}}$

Output

Output a total of $t$ lines, where $t$ represents the number of different sequences. Each line outputs two numbers $l$ and $r$ (both greater than $0$), indicating the starting and ending numbers of the sequence. Note that when there are multiple sequences, they should be outputted in descending order based on $l$. If there is no answer, DO NOT output anything.

Sample Input 1

27

Sample Output 1

13 14
8 10
2 7

$13+14=8+9+10=2+3+\cdots+6+7=27$.

Sample Input 2

69

Sample Output 2

34 35
22 24
9 14

$\sum_{i=34}^{35}i=\sum_{i=22}^{24}i=\sum_{i=9}^{14}i=69$.