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
import sys
from collections import *
from math import *
import re
def sieve(n):
    prime=[True for i in range(n+1)]
    p=2
    while p*p<=n:
        if prime[p]==True:
            for i in range(p*p,n+1,p):
                prime[i]=False
        p+=1
    c=0
    for i in range(2,n):
        if prime[i]:
            #print(i)
            c+=1
    return c

def iseven(n):return[False,True][0 if n%2 else 1]
def inp_arr():return list(map(int,input().split()))
def inp():return map(int,input().split())
def lcm(a,b):return (a*b)/gcd(a,b)
max_int = sys.maxsize
mod = 10**9+7

an=[n*(n+1)/2 for n in range(1,501)]
n=int(input())
print('YES' if n in an else 'NO')