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:
t = int(input())


def find_one_factor(num, a):
    for i in range(2, int(num ** 0.5) + 1):
        if num % i == 0:
            if a == i:
                continue
            return i, num // i

    return -1, -1


while t:
    t -= 1
    n = int(input())
    flag = True
    factors = []

    a, num = find_one_factor(n, 0)
    if a == -1:
        print("NO")
        continue
    b, num = find_one_factor(num, a)
    if b == -1:
        print("NO")
        continue
    elif b == num:
        print("NO")
        continue

    c = num

    print("YES")
    print("{} {} {}".format(a, b, c))