Triangular numbers

Time Limit: 2 seconds

Memory Limit: 256 megabytes

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. . 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.

Sample Input

Input
1
Output
YES
Input
2
Output
NO
Input
3
Output
YES

Sample Output

None

Hint

None

Source

None

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