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:
def foo(num):
    isSimple = True
    k = 0
    while k < arr.__len__() and arr[k] <= math.sqrt(num):
        if num % arr[k] == 0:
            isSimple = False
            num = num / arr[k]
            break
        k += 1
    return num

import math
n = int(input())


arr = []

root = math.sqrt(1000000000)
for num in range(2, int(root) + 1):
    isSimple = True
    for delimiter in range(2, int(math.sqrt(num)) + 1):
        if num % delimiter == 0:
            isSimple = False
            break
    if isSimple:
        arr.append(num)



for i in range(n):
    
    num = int(input())
    res = foo(num)
    if res == num:
        print("NO")
        continue
    else:
        d1 = num / res
        num = res

    res = foo(num)
    if res == num:
        print("NO")
        continue
    else:
        d2 = num / res
        num = res

    if d1 == d2: 
        res = foo(num)
        if res == num:
            print("NO")
            continue
        d2 *= num / res
        num = res

    if d1 != num and d2 != num and d1 != d2:
        print("YES")
        print("%d %d %d" % (d1, d2, res))
    else:
        print("NO")