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. <image>. 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
a=int(input())
if a==1 or a==3 or a==6 or a==10 or a==15 or a==21 or a==28 or a==36 or a==45 or a==55 or a==66 or a==78 or a==91 or a==105 or a==120 or a==136 or a==153 or a==171 or a==190 or a==210 or a==231 or a==253 or a==276 or a==300 or a==325 or a==351 or a==378 or a==406 or a==435 or a==465 or a==496:
    print('YES')
else:
    print('NO')