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().strip())
import math

for t in range(T):
    N = int(input().strip())
    status = True
    for a in range(2, int(math.sqrt(N)+1)):
        if N%a==0:
            b=N//a
            for x in range(2, int(math.sqrt(b)+1)):
                if x!=a and b%x==0 and a!=b//x and x!=b//x:
                    print('YES')
                    print(a, x, b//x)
                    status=False
                    break
        if status==False:
            break
    if status==True:
        print('NO')