Problem Description

Translated from ROIR 2020 Day1 T1. Разность квадратов, translator ShineEternal

You are involved in developing a module for a symbolic computation system. It will be used to solve a special type of Diophantine equation, described as follows:

Given a non-negative integer $n$, the module under development needs to find two positive integers $x$ and $y$ such that $x^2-y^2=n$, where $x,y$ do not exceed $2^{62}-1$.

You need to write a program that, for a given non-negative integer $n$, finds two natural numbers $x$ and $y$ such that both of them do not exceed $2^{62}-1$ and their difference of squares is $n$.

Input Format

One line with one integer $n$.

Output Format

If such $x,y$ exist, print two lines. The first line should be the single string Yes. The second line should print any one pair $x,y$.

If no such pair exists, output No.

3

Yes
2 1

2

No

Hint

For $100\%$ of the testdata, $0\le n\le 2^{60}$.

Constraints

Translated by ChatGPT 5