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:
from math import sqrt
def solve(n):
    if isprime(n,2)==-1:return 'NO'
    i=2
    while i<=sqrt(n):
        if n%i==0:
            p=isprime(n//i,i+1)
            if p!=-1:return i,p
        i+=1
    return 'NO'
def isprime(n,b):
    i=b
    while i<=sqrt(n):
        if n%i==0 and i!=n//i:return i,n//i
        i+=1
    return -1
for _ in range(int(input())):
    n=int(input());s=solve(n)
    if s=='NO':print(s)
    else:print('YES');print(s[0],*s[1])