#83 ronaldo

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#83 ronaldo | DOJ

Time limit: 1000 ms
Memory limit: 1024 MB
Checker: CUSTOM
Solve threshold: 100

Statement

The title has nothing to do with the problem. The title is named after a football player that problem setter likes, Cristiano Ronaldo.

Given a positive integer $N$ , determine whether $N$ can be expressed as the sum of two or more consecutive positive integers. That is, determine whether there exists an integer pair $(S, L)$ satisfying:

$N =S+(S+1)+(S+2)\dots+(S+L-1)$
$S \geq 1$
$L \geq 2$

Input

A positive integer $N$ is given on the first line.

Output

Print YES if an integer pair $(L,S)$ satisfying the given conditions exists, and NO otherwise.

Constraints

$1 \leq N \leq 10^{18}$ .

Subtasks

#	Score	Constraints
1	4	$N=1$ .
2	9	$N \leq 100$ .
3	13	$N$ is an odd number.
4	34	There is an integer $n$ such that $N = 2 \times(2n+1)$ .
5	40	No additional constraints.

Samples

Sample 1

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Output

Sample 2

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Sample 3

Input

Output

YES