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 PYTHON):

Solution:
from sys import stdin
t = int(stdin.readline())
 
for _ in xrange(t):
    n = int(stdin.readline())
    a = []
    i = 2
    while True:
        if i * i > n:
            break
        if n%i==0:
            a.append(i)
            n/=i
            i+=1
            break
        i+=1

    while True:
        if i*i > n:
            break
        if n%i==0:
            a.append(i)
            a.append(n/i)
            break
        i+=1
    a = list(set(a))
    if len(a)==3:
        print "YES"
        print a[0],a[1],a[2]
    else:
        print "NO"