Triangular numbers

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.

Examples

Input

1

Output

YES

Input

2

Output

NO

Input

3

Output

YES

inputFormat

Input

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

outputFormat

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

样例

2

NO

</p>