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:
from math import sqrt
def calcul(x,message):
    for j in range (2,int(sqrt(x))):
        if x%j==0:
            m=x/j
            s=int(sqrt(m))
            if j+1>s: 
                s=int(m/2)
            for  k in range (j+1,s+1):
                if (m%k==0) and (int(m/k)!=k) and (int(m/k)!=j):
                    message="YES"
                    print(message)
                    print(j,' ',k,' ',int(m/k))
                    return -1
n = int(input())

for i in range (0,n):
    x=(int(input()))
    message="NO"
    if calcul(x,message)!=-1:
        print(message)