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 
import math
n=int(input())
for i in range(n):
    l=[]
    trigger=0
    a=int(input())
    d=0
    original=a
    c=int(math.sqrt(a))
    for j in range(2,c+1):
        if a%j==0:
            l.append(j)
            a=a//j
            trigger+=1
        if trigger==2:
            if a<original and l[0]!=a and l[1]!=a and original%a==0:
                l.append(a)
                print("YES")
                print(*l,sep=" ")
                d+=1
                break
    if d==0:
        print("NO")