Migrated from Lutece 334 Triangular numbers

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Description

A triangular number is the number of dots in an equilateral triangle uniformly filled with dots. For example, three dots can be arranged in a triangle; thus three is a triangular number. The $n_{th}$ triangular number is the number of dots in a triangle with n dots on a side.

Your task is to find out if a given integer is a triangular number.

Input

There are multi-cases, for each case there is only a single number $n$ ($1\leq  n\leq  500$) — the given integer.

Output

For each case, if the given integer is a triangular number output YES, otherwise output NO.

Samples

1
2
3

YES
NO
YES

Resources

2011寒假训练（一）(Not Original)