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Find the Fraction

Time limit0.5sMemory limit256 MB

Summary

Given an index X, determine which fraction r/c appears at that position when all fractions r/c are enumerated in a zigzag diagonal order.

Level: Medium4 of 10
Topics: Math, Simulation
Solved: No attempts yet

Problem

In an infinite table, the cell in row r and column c contains the fraction r/c.


1/1	1/2	1/3	1/4	1/5	...
2/1	2/2	2/3	2/4	...	...
3/1	3/2	3/3	...	...	...
4/1	4/2	...	...	...	...
5/1	...	...	...	...	...
...	...	...	...	...	...

The fractions are read in a zigzag order along diagonals: 1/1, 1/2, 2/1, 3/1, 2/2, and so on.

Given an integer X, print the X-th fraction in this order.

Input

The first line contains an integer X. (1 <= X <= 10,000,000)

Output

Print the X-th fraction in numerator/denominator format on the first line.

Examples10

Example 1
Input
```
1
```
Expected output
```
1/1
```
Example 2
Input
```
2
```
Expected output
```
1/2
```
Example 3
Input
```
3
```
Expected output
```
2/1
```
Example 4
Input
```
4
```
Expected output
```
3/1
```
Example 5
Input
```
5
```
Expected output
```
2/2
```
Example 6
Input
```
6
```
Expected output
```
1/3
```
Example 7
Input
```
7
```
Expected output
```
1/4
```
Example 8
Input
```
8
```
Expected output
```
2/3
```
Example 9
Input
```
9
```
Expected output
```
3/2
```
Example 10
Input
```
14
```
Expected output
```
2/4
```

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