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 szuk_podz(liczba, a = 1):
    for x in range(2, int(sqrt(liczba)) + 1):
        if liczba % x == 0 and x != a:
            return x
    return -1
for _ in range(int(input())):
    n = int(input())
    a, b, c = szuk_podz(n), 0, 0
    x = n // a
    if a == -1:
        print("NO")
        continue
    b = szuk_podz(x, a)
    c = x // b
    if c == a or c == b:
        print("NO")
        continue
    if c > 0 and b > 0:
        print("YES")
        print(a, b, c)
    else:
        print("NO")