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:
"""T=int(input())
for _ in range(0,T):
    n=int(input())
    a,b=map(int,input().split())
    s=input()
    s=[int(x) for x in input().split()]
    for i in range(0,len(s)):
        a,b=map(int,input().split())"""

import math
T=int(input())
for _ in range(0,T):
    N=int(input())
    n=N
    L=[]
    while (n % 2 == 0):
        L.append(2)
        n = n // 2
        
    for i in range(3,int(math.sqrt(n))+1,2): 
        while (n % i== 0):
            L.append(i)
            n = n // i 

    if (n > 2): 
        L.append(n)

    if(len(L)<3):
        print('NO')
    else:
        t1=L[0]
        t2=L[1]
        t3=1
        if(L[1]==L[0]):
            t2=L[1]*L[2]
            for j in range(3,len(L)):
                t3*=L[j]
        else:
            for j in range(2,len(L)):
                t3*=L[j]
        if(t1!=t2 and t2!=t3 and t1!=t3 and t1>1 and t2>1 and t3>1):
            print('YES')
            print(t1,t2,t3)
        else:
            print('NO')