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 *

for _ in range(int(input())):
    n = int(input())
    nn = n
    l = []
    now = 2
    m = []
    sq = int(sqrt(n))
    
    while n > 1:
        if n % now == 0:
            while n % now == 0:
                l.append(now)
                n //= now
        else:
            now += 1

        if now > sq:
            break

    if len(l) < 2:
        print("NO")
        continue

    m.append(l[0])

    if l[0] != l[1]:
        m.append(l[1])
    elif len(l) == 2:
        print("NO")
        continue
    else:
        m.append(l[1] * l[2])

    t = nn // (m[0] * m[1])

    if (t == 1) or (t in m):
        print("NO")
        continue
    else:
        print("YES")
        print(m[0], m[1], t)