Problem: You are given one integer number n. Find three distinct integers a, b, c such that 2 ≤ a, b, c and a ⋅ b ⋅ c = n or say that it is impossible to do it.

If there are several answers, you can print any.

You have to answer t independent test cases.

Input

The first line of the input contains one integer t (1 ≤ t ≤ 100) — the number of test cases.

The next n lines describe test cases. The i-th test case is given on a new line as one integer n (2 ≤ n ≤ 10^9).

Output

For each test case, print the answer on it. Print "NO" if it is impossible to represent n as a ⋅ b ⋅ c for some distinct integers a, b, c such that 2 ≤ a, b, c.

Otherwise, print "YES" and any possible such representation.

Example

Input


5
64
32
97
2
12345


Output


YES
2 4 8 
NO
NO
NO
YES
3 5 823 

Solution (in PYTHON3):

Solution:
import math
from collections import Counter

def primeFactors(n): 
    ans = []
    while n % 2 == 0: 
        ans.append(2) 
        n = n//2
    for i in range(3,int(math.sqrt(n))+1,2): 
        while n % i== 0: 
            ans.append(i)
            n = n // i 
    if n > 2: 
        ans.append(n)
    return ans
def prod(a):
    ans = 1
    for i in a:
        ans*=i
    return ans

for _ in range(int(input())):
    n = int(input())
    a = primeFactors(n)
    if len(a)<3:
        print("NO")
    else:
        c = Counter(a)
        if len(set(a))<3:
            if len(c)==1:
                if c[a[0]]>=6:
                    print("YES")
                    print(a[0],a[0]*a[0],a[0]**(c[a[0]]-3))
                else:
                    print("NO")
            else:
                if len(a)>=4:
                    print("YES")
                    print(a[0],a[-1],prod(a[1:-1]))
                else:
                    print("NO")
        else:
            w = list(set(a))
            print("YES")
            print(w[0],w[1],prod(a)//(w[0]*w[1]))