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:
def f1(x,k):
    for i in range(int(math.sqrt(x)),1,-1):
        if (x%i==0):
            y=x//i
            if (i!=y) and (i!=k) and (y!=k):
                return i
    return 0
 
import math
t=int(input())
for i in range(t):
    n=int(input())
    if (n<24):
        print("NO")
        continue
    a=0
    b=0
    c=0
    for j in range(int(pow(n,1/3)),1,-1):
        if (n%j==0):
            p=n//j
            z=f1(p,j)
            if (z!=0):
                a=j
                b=z
                c=p//z
                break
    if (a!=0):
        print("YES")
        print(a,b,c)
    else:
        print("NO")