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:
#!/usr/bin/env python3
import math

primes = [2]

for n in range(3,math.ceil(math.sqrt(1e9)),2):
    is_prime = True
    sqrt_n = math.sqrt(n)
    for p in primes:
        if p > sqrt_n:
            break 
        if n%p == 0:
            is_prime = False
            break
    if is_prime:
        primes.append(n)

t = int(input())
for _ in range(t):
    n = int(input())
    _n = n
    factors = {}
    for p in primes:
        while _n % p == 0:
            if p not in factors:
                factors[p] = 0
            factors[p] += 1
            _n /= p
    if _n != 1:
        factors[_n] = 1

    f1 = None
    f2 = None
    if len(factors) == 1:
        [f] = list(factors)
        if factors[f] >= 6:
            f1 = f
            f2 = f*f
    elif len(factors) == 2:
        [_f1, _f2] = list(factors)
        if (factors[_f1] + factors[_f2]) >= 4:
            f1 = _f1
            f2 = _f2 
    elif len(factors) >= 3:
        [_f1,_f2] = list(factors)[:2]
        f1 = _f1
        f2 = _f2

    if f1 != None and f2 != None:
        print("YES")
        print(f"{int(f1)} {int(f2)} {int(n/(f1*f2))}")
    else:
        print("NO")