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
def isTriangular(num):

	# Base case
	if (num < 0):
		return False

	# A Triangular number must be
	# sum of first n natural numbers
	sum, n = 0, 1

	while(sum <= num):
	
		sum = sum + n
		if (sum == num):
			return True
		n += 1

	return False

# Driver code
n = int(input())
if (isTriangular(n)):
	print("YES")
else:
	print("NO")

# This code is contributed by Smit
