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 primeFactors(n):
    f = []
    while n % 2 == 0: 
        f.append(2), 
        n = n / 2
    for i in range(3,int(math.sqrt(n))+1,2):
        while n % i== 0: 
            f.append(i), 
            n = n / i
    if n > 2:
        f.append(n)

    return f

t = int(input())

while t>0:
    n = int(input())

    l = primeFactors(n)
    s = list(set(l))
    ss = len(s)
    sl = len(l)

    if sl<=2:
        print('NO')

    elif ss==1 and sl<6:
        print('NO')

    elif ss==2 and sl<4:
        print('NO')

    else:
        if ss>=2:
            l1 = [int(s[0]),int(s[1]),int(n/(s[0]*s[1]))]
            print('YES')
            print(*l1)
        else:
            l2 = [int(s[0]),int(s[0]*s[0]),int(n/(s[0]*s[0]*s[0]))]
            print('YES')
            print(*l2)

    t-=1