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:
import math
t = int(input())
for i in range(t):
    a = 0
    b = 0
    n = int(input())
    for j in range (int(math.sqrt(n))-1):
        if n%(j+2) == 0:
            n = n//(j+2)
            a = j+2
            break
    if a == 0:
        print("NO")
    elif a != 0:
        for j in range (int(math.sqrt(n))-2):
            if n%(j+3) == 0 and j+3 != a:
                n = n//(j+3)
                if n != j+3:
                    b = j+3
                    break

        if b == 0:
            print("NO")
        else:
            print("YES")
            print(a, b, n)