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
number = [0] * 32
n = int(input())
i = 1
for i in range(0, 32):
    number[i] = (i * (i + 1)) // 2

mid = 16
left = 0
right = 31

while number[mid] != n and left <= right:
    if n > number[mid]:
        left = mid + 1
    else:
        right = mid - 1
    mid = (left + right) // 2

if left > right:
    print('NO')
else:
    print('YES')
