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
for _ in range(int(input())):
    n = int(input())
    d = {}
    x = int(math.sqrt(n))
    ans = []
    flag  = 0
    product = 1
    for i in range(2,x+1):
        if n%i==0:
            product*=i
            if n%product==0:
                ans.append(i)
            else:
                product/=i
            flag = 1
        if len(ans)==2:
            break
    if flag == 1 and len(ans)>=2:
        y = n//(ans[-1]*ans[-2])
        if y in ans or n%y!=0:
            print("NO")
        else:
            print("YES")
            ans.append(y)
            for i in ans:
                print(i,end=" ")
            print()
 
    else:
        print("NO")