[Solution] Garage Codeforces Solution

[Solution] Garage Codeforces Solution | Solution Codeforces

G. Garage

time limit per test

1 second

memory limit per test

128 megabytes

input

standard input

output

standard output

Pak Chanek plans to build a garage. He wants the garage to consist of a square and a right triangle that are arranged like the following illustration.

Define 𝑎$a$ and 𝑏$b$ as the lengths of two of the sides in the right triangle as shown in the illustration. An integer 𝑥$x$ is suitable if and only if we can construct a garage with assigning positive integer values for the

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 lengths 𝑎$a$ and 𝑏$b$ (𝑎<𝑏$a<b$) so that the area of the square at the bottom is exactly 𝑥$x$. As a good friend of Pak Chanek, you are asked to help him find the 𝑁$N$-th smallest suitable number.

Input

The only line contains a single integer 𝑁$N$ (1≤𝑁≤109$1\le N\le {10}^9$).

Output

An integer that represents the 𝑁$N$-th smallest suitable number.