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 sys
import time 
import math
start_time = time.time()

input = sys.stdin.readline



t = int(input())
for _ in range( t):
    n = int(input())
    sqrtn = math.ceil(n**0.5)
    a,b,c=1,1,1
    
    mod = 2
    
    while(True):
        if n == 1 or mod > sqrtn:
            break
        if n % mod == 0 :
            if a == 1 :
                a*= mod
            else:
                b*= mod
            n//= mod
            if(a>1 and b > 1 and a!= b):
                c = n 
                break
        else:
            if mod == 2 :
                mod  = 3
            else:
                mod += 2
                

    # print(a,b,c)
    if(a==1 or b==1 or c==1 or a==b or b==c or a==c):
        print("NO")
    else:
        print("YES")
        print(a,b,c)
    
# print("--- %s seconds ---" % (time.time() - start_time))