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())
    
    #if n < 24:
    #    print('NO')
   
    a = 0
    b = 0
    c = 0
    sqrt = int(n ** 0.5)
    for i in range(2, sqrt + 1):
        if n % i == 0:
            a = i
            n /= a
            break
    if a:
        for i in range(a +1, int(n ** 0.5) + 1):
            if n % i == 0:
                b = i
                c = int(n // i)
                break

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