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())

for _ in range(t):
    n = int(input())

    factors = []
    i = 2
    while i * i <= n:
        while n % i == 0:
            factors.append(i)
            n //= i
        i += 1
    if n > 1:
        factors.append(n)

    # print(factors)
    if len(factors) < 3:
        print("NO")
    else:

        i = 0
        a = factors[i]
        i += 1
        b = factors[i]
        i += 1
        while i < len(factors) and b == a:
            b *= factors[i]
            i += 1
            if b != a:
                break
        if i == len(factors):
            print("NO")
        else:
            c = factors[i]
            i += 1
            while i < len(factors):
                c *= factors[i]
                i += 1

            if c != a and c != b:
                print("YES")
                print(a, b, c)
            else:
                print("NO")