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 
import math

def GetNumber(start, n, number, count):
    if count == 1 and n >= start:
        number += (str(n))
        print("YES")
        print(number)
        return 
    for i in range(start, int(math.sqrt(n)) + 1):
        if n % i == 0:
            number += (str(i)+" ")
            count -= 1
            GetNumber(i+1, int(n / i), number, count)
            return
    print("No")
    return



inputCount = int(input(""))

for i in range(0, inputCount):
    n = int(input(""))
    GetNumber(2, n, "", 3)