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
def solve(n):
    root=int(math.sqrt(n))
    a=-1
    b=-1
    c=0
    i=2
    while(i<=root):
        if(n%i==0):
            a=i
            n=n/i
            break
        i=i+1
    root=int(math.sqrt(n))
    i=2
    while(i<=root):
        if(n%i==0 and i!=a and n/i!=a and i!=n/i):
            b=i
            c=int(n/i)
            break
        i=i+1
    if(a==-1 or b==-1):
        print("NO")
    else:
        output="{0} {1} {2}"
        print("YES")
        print(output.format(a,b,c))
t=int(input())
while(t>=1):
    n=int(input())
    solve(n)
    t=t-1