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:
import math

def mul3(n):
    original_n = n
    divisors = set()
    divisor = 2
    sqrt_n = int(math.sqrt(n))
    while divisor <= sqrt_n and len(divisors) < 2:
        if n % divisor == 0: 
            divisors.add(divisor)
            n //= divisor
        divisor += 1

    if len(divisors) < 2:
        return None

    list_divisors = list(divisors)
    multiplication = list_divisors[0] * list_divisors[1]
    third_number = original_n // multiplication

    if third_number in divisors:
        return None

    return divisors | set([third_number])
    
# 24 -> 2, 3, 4
# 8 -> None
# 7 -> None
# 6 -> None
# 13 * 17 * 19 -> 13, 17, 19 

number_of_tests = int(input())
for _ in range(number_of_tests):
    n = int(input())
    result = mul3(n)
    if not result:
        print('NO')
        continue
    print('YES')
    print(' '.join(map(str, result)))