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):
    f = 0
    n = int(input())
    if n % 2 == 0:
        a = 2
        f = 1
    else:
        for j in range(3 ,int((n**(1/3)) + 2), 2):
            if (n % j == 0):
                a = j
                f = 1
                break
    
    if (f == 0):
        print("NO")
    else:
        n = n // a
        f = 0
        for j in range(a ,int((n**(1/2)) + 2)):
            c = n // j
            if (n % j == 0) and (j !=  a) and (c) != 1:
                b = j
                f = 1
                break
        if (f == 0) or (b == c) or (a == c):
            print("NO")
        else:
            print("YES")
            print(a, b, c)