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:
import math
def ans(n):
    a, b = -1, -1
    for i in range(2, int(math.sqrt(n)) + 1):
        if n % i == 0:
            a = i 
            break
    if a == -1:
        print('NO')
        return
    for i in range(a + 1, int(math.sqrt(n)) + 1):
        if (n % i == 0) & (n % (a * i) == 0):
            b = i
            break
    if b == -1:
        print('NO')
        return
    if (n / (a * b) != 1) & (n / (a * b) != a) & (n / (a * b) != b):
        print('YES')
        print(a, b, int(n / (a * b)))
        return
    print('NO')
    return

t = int(input())
while(t):
    t = t - 1 
    n = int(input())
    ans(n)