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:
R = lambda:map(int, input().split(" "))
from math import sqrt

def divs(n):
    a, b, c = 2, 2, 2
    while a <= sqrt(n):
        if n % a == 0:
            n //= a
            break
        a += 1
    b = a + 1
    while b <= sqrt(n):
        if n % b == 0:
            c = n // b
            if c == a or c == b:
                break
            print("YES")
            print(a, b, c)
            n //= b
            return
        b += 1
    print("NO")

t = int(input())
for i in range(t):
    n = int(input())
    divs(n)