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
n = int(input())
for _ in range(n):
    a = 0
    b = 0
    k = int(input())
    for i in range(2,int(sqrt(k))+1):
        if k%i == 0:
            a = i
            break
    if a > 0:
        temp = int(sqrt(k/a+1))
        for i in range(a+1,temp+1):
            if (k/a) % i == 0:
                b = i
                break
    if a==0 or b==0:
        print("NO")
    elif(k/(a*b) > b):
        print("YES")
        print(a,b,int( k/(a*b) ) )
    else:
        print("NO")

    #print(a,b,c,k)