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 collections import defaultdict
for _ in range(int(input())):
    n = int(input())
    dr = n
    i = 2
    primes = defaultdict(int)
    while i * i <= n:
        while dr % i == 0:
            primes[i] += 1
            dr //= i
        i += 1
    if dr != 1:
        primes[dr] += 1
    if len(primes) >= 3:
        print("YES")
        i = 0
        for par in primes:
            print(par, end=" ")
            n //= par
            i += 1
            if i == 2:
                break
        print(n)
    elif len(primes) == 2:
        primes = [(k, v) for k, v in primes.items()]
        if primes[0][1] == 1:
            if primes[1][1] <= 2:
                print("NO")
                continue
            else:
                print("YES")
                print(primes[0][0], primes[1][0], n // (primes[0][0] * primes[1][0]))
        elif primes[1][1] == 1:
            if primes[0][1] <= 2:
                print("NO")
                continue
            else:
                print("YES")
                print(primes[0][0], primes[1][0], n // (primes[0][0] * primes[1][0]))
        else:
            print("YES")
            print(primes[0][0], primes[1][0], n // (primes[0][0] * primes[1][0]))
    else:
        primes = [(k, v) for k, v in primes.items()]
        primes = primes[0]
        if primes[1] >= 6:
            print("YES")
            print(primes[0], primes[0] ** 2, n // (primes[0] ** 3))
        else:
            print("NO")