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
# your code goes here
def getTraingleNumbers():
	a = []
	number = 1
	start = 1
	while number <= 500:
		number = int((start*(start+1))/2)
		a.append(number)
		start += 1
	return a
n = int(input())
array = getTraingleNumbers()
result = "NO"

for i in range(len(array)):
	if array[i] == n:
		result = "YES"
		break
print(result)
