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())
    sq = int(math.sqrt(n))
    l = []
    f = 0
    for j in range(2,sq):
        if n%j==0:
            n = n//j
            l.append(j)
            f = j
            if len(l) == 2:
                break
            elif j>n:
                break
            else:
                f = j
    if len(l) == 2:
        if n>j:
            l.append(n)
            print("YES")
            for x in l:
                print(x,end=" ")
            print()
        else:
            print("NO")
    else:
        print("NO")