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:
import sys
input = sys.stdin.readline

def find(n,fa,fb):
    f = 2
    while f*f <= n:
        if n % f == 0 and f != fa and f != fb:
            return f
        f += 1
    return n

for _ in xrange(int(input())):
    n = int(input())
    nn = n
    fa = find(n,None,None)
    n = n // fa
    fb = find(n,fa, None)
    fc = nn // fa // fb

    if fa*fb*fc == nn and fa >= 2 and fb >= 2 and fc >= 2 and fa != fb and fa != fc and fb != fc:
        print("YES")
        print fa,fb,fc
    else:
        print("NO")