N. Ma3rofa 2lsra7a
time limit per test
1 second
memory limit per test
1024 megabytes
input
standard input
output
standard output

Gohary and Tawfik are arguing about number theory. Gohary claims that any number can be expressed as the sum of three perfect squares, but Tawfik disagrees and challenges him to prove it.

Given a positive integer $$$x$$$, determine whether there exist integers $$$a$$$, $$$b$$$, and $$$c$$$ such that: $$$$$$a^2 + b^2 + c^2 = x$$$$$$ where $$$1 \leq a \leq b \leq c$$$.

Help Gohary settle this debate by determining if such a representation exists!

Input

The input consists of a single integer $$$x$$$ ($$$1 \leq x \leq 10^{8}$$$) — the target sum.

Output

Output YES if there exist integers $$$a$$$, $$$b$$$, $$$c$$$ with $$$1 \leq a \leq b \leq c$$$ such that $$$a^2 + b^2 + c^2 = x$$$.

Output NO otherwise.

Note

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