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

t = int(input())
for j in range(t):
    n = int(input())
    m = 0
    bul_1 = False
    bul_2 = False
    i = 2
    while i <= int(sqrt(n)):
        if n % i == 0:
            if bul_1:
                bul_2 = True
                if i != n // i:
                    print("YES")
                    print(m, i, n // i)
                else:
                    print("NO")
                break
            else:
                m = i
                bul_1 = True
                n //= i
        i += 1
    if not bul_2:
        print("NO")