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:
from math import sqrt
def factorize3(n):
    f, s = 1, 1
    for i in range(2, int(sqrt(n)) + 1):
        if n % i == 0:
            f = i
            n = n // i
            break
    for i in range(f + 1, int(sqrt(n)) + 1):
        if n % i == 0:
            s = i
            n = n // i
            break
    if s != n and f != 1 and s != 1:
        print("YES")
        print(f, s, n)
    else:
        print("NO") 


test_size = int(input())
for i in range(test_size):
    n = int(input())
    factorize3(n)