Source

This problem is adapted from Long Long OJ. All rights reserved.

Description

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.

Input

An integer $N$.

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.

Samples

27

13 14
8 10
2 7

69

34 35
22 24
9 14

Tips

Sample Explanation 1:

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

Sample Explanation 2:

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

• For $50\%$ of the testcases, $1\leq N\leq 10^{6}$.
• For $100\%$ of the testcases, $1\leq N\leq 10^{16}$.