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 as s


def factorization(n):
    a=[]
    while n%2==0:
        a.append(2)
        n = n//2

    for i in range(3,int(s(n))+1,2):
        while n%i==0:
            a.append(i)
            n = n//i
                    
    if n>2:
        a.append(n)
    return a

for i in range(int(input())):
    n = int(input())
    a = factorization(n)

    flag='hobe'
    
    if len(a)<3:
        flag='miao'
    else:
        res = []
        res.append(a[0])

        if a[1]==a[0]:
            res.append(a[1]*a[2])
            j=3
        else:
            res.append(a[1])
            j=2

        temp=1
        for i in range(j,len(a)):
            temp=temp*a[i]
            
        if temp in res or temp==1:
            flag='miao'
        else:
            res.append(temp)

    if flag=='miao':
        print('NO')
    else:
        print('YES')
        print(*res)