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:
"""
Author: guiferviz
Time: 2020-02-08 17:10:34
"""


def prime_factors(n):
    factors = []

    while n % 2 == 0:
        n //= 2
        factors.append(2)

    for i in range(3, int(n**0.5 + 1), 2):
        while n % i == 0:
            n //= i
            factors.append(i)

    if n != 1:
        factors.append(n)

    return factors


def solve():
    n = int(input())
    f = prime_factors(n)
    a, b, c = 1, 1, 1
    for i in f:
        if a == 1:
            a = i
        elif b == 1 or a == b:
            b *= i
        else:
            c *= i

    sol = False
    if a * b * c == n and a != b and b != c and a != c and b > 1 and c > 1:
        sol = True

    if sol:
        print("YES")
        print(a, b, c)
    else:
        print("NO")


def main():
    t = int(input())
    for _ in range(t):
        solve()


if __name__ == "__main__":
    main()