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. . You can learn more about these numbers from Wikipedia (http://en.wikipedia.org/wiki/Triangular_number).

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

Input

The first line contains the single number $*n*$ ($1 ≤ *n* ≤ 500$) — the given integer.

Output

If the given integer is a triangular number output YES, otherwise output NO.