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 i in range(t):
    n = int(input())
    ans = 'NO'
    p = q = 1
    for j in range(2, int(n ** (1 / 3)) + 2):
        if n % j == 0:
            p = j
            n = n // p
            ans = 'YES'
            break
    if ans == 'YES':
        ans = 'NO'
        for j in range(p + 1, int(n ** (1 / 2)) + 2):
            if n % j == 0:
                q = j
                n = n // q
                ans = 'YES'
                break
    if n <= q:
        ans = 'NO'
    print(ans)
    if ans == 'YES':
        print(p, q, n)