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
t = int(input())
while t > 0:
    n = int(input())
    fact = []
    for i in range(2, int(math.sqrt(n))+1):
        if i*int(n/i) == n:
            if i != int(n/i):
                fact.append(i)
                fact.append(int(n/i))
            else:
                fact.append(i)
    fact.sort()
    flag = 0
    for i in range(len(fact)-1):
        for j in range(i+1, len(fact)):
            if fact[i]*fact[j] < n and (n % (fact[i]*fact[j]) == 0):
                num = int(n/(fact[i]*fact[j]))
                if num != fact[i] and num != fact[j]:
                    flag = 1
                    break
        if flag == 1:
            break
    if flag == 0:
        print('NO')
    else:
        print('YES')
        print(fact[i], fact[j], num)
    t -= 1