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(0,t):
    n=int(input())
    n1=0
    n2=0
    n3=0
    for j in range(2,int(math.ceil((math.sqrt(n))))):
        if n%j==0:
            n1=j
            n3=n/j
            break
        else:
            continue
    z=0
    for j in range(n1+1,(int(math.ceil((math.sqrt(n3)))))):
        if n3%j==0 and j!=n3/j and (n3/j)!=n1:
            z=1
            n2=j
            n3=int(n3/j)
            break
        else:
            continue
    if z==0:
        print("NO")
    else:
        print("YES")
        print(n1,n2,n3)