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
t=int(input())
for i in range(t):
    n=int(input())
    a=math.sqrt(n)
    a=int(a)
    c=[]
    f=0
    d=0
    b=int(a)
    for j in range(2,a+1,1):
        if(n%j==0):
              f=1
              x=j
              y=n//j
              break 
    if(f==0):
        print("NO")
    else:
        f=0
        for j in range(2,int(y**(1/2))+1):
            if(y%j==0):
                if(x!=j and y//j!=x and y//j!=j):
                    z=j
                    y=y//j
                    f=1
                    break
        if(f==0):
            print("NO")
        else:
            print("YES")
            print(x,y,z)