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A. Triangular numbers

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputA 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.

Examples

Input

1

Output

YES

Input

2

Output

NO

Input

3

Output

YES

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