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())
for q in range(t):
    n=int(input())
    m=n
    fact=[]
    while m%2==0:
        fact.append(2) 
        m = m / 2
    for i in range(3,int(math.sqrt(m))+1,2): 
        while m % i== 0: 
            fact.append(i) 
            m = m / i 
    if m > 2: 
        fact.append(m)
    dist = list(set(fact))
    if len(dist)==1:
        if fact.count(dist[0])>4:
            o=dist[0]
            t=dist[0]*dist[0]
            if (n/(o*t))>2 and int((n/(o*t)))!=o and int((n/(o*t)))!=t:
                print('YES')
                print(int(o),int(t),int((n/(o*t))))
            else:
                print('NO')
        else:
            print('NO')
    elif len(dist)==2:
        o=dist[0]
        t=dist[1]
        if (fact.count(o)+fact.count(t))>=4:
            if (n/(o*t))>2 and int((n/(o*t)))!=o and int((n/(o*t)))!=t:
                print('YES')
                print(int(o),int(t),int((n/(o*t))))
            else:
                print('NO')
        else:
            print('NO')
    if len(dist)>2:
        o=dist[0]
        t=dist[1]
        if (n/(o*t))>2 and int((n/(o*t)))!=o and int((n/(o*t)))!=t:
            print('YES')
            print(int(o),int(t),int((n//(o*t))))
        else:
            print('NO')