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

n = int(input())
for i in range(n):
    q = int(input())
    qq = q
    for i in range(2, int(sqrt(q)) + 1):
        if q % i == 0:
            a = i
            q //= i
            break
    else:
        print("NO")
        continue
    for i in range(a + 1, int(sqrt(q)) + 1):
        if q % i == 0:
            b = i
            c = qq // (a * b)
            break
    else:
        print("NO")
        continue
    
    if a == b or b == c or a == c:
        print("NO")
        continue
    print("YES")
    print(a, b, c)