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:

    
for _ in range(int(input())):
    n=int(input())
    a=b=c=1
    for i in range(2,int(n**0.5)+1):
        if(n%i == 0):
	            a=i
	            n//=i
	            break
    for i in range(2,int(n**0.5)+1):
        if(n%i == 0):
	            if(i!=a):
	                b=i
	                n//=i
	                break
    if(n!=1 and n!=a and n!=b):
        	c=n
    if(a==1 or b==1 or c==1):
        print("NO")
    else:
        print("YES")
        print(a,b,c,sep=" " )