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
def splitPrime(n):
    arr = {}
    for i in range(2, math.ceil((math.sqrt(n))) + 1):
        while n != 0 and n % i == 0:
            f = arr.get(i, 0)
            arr[i] = int(f + 1)
            n = n // i
    if n > 1:
        arr[n] = 1
    return arr

t = int(input())
for i in range(t):
    n = int(input())
    arr = splitPrime(n)
    numbersKey = len(arr)
    if numbersKey >= 3:
        print('YES')
        count = 0
        result = 1
        for key in arr:
            if count == 2:
                break
            print(key, end=' ')
            result *= key
            count += 1
        print(n // result)
    elif numbersKey == 2 and sum(arr.values()) >= 4:
        print('YES')
        result = 1
        for key in arr:
            print(key, end=' ')
            result *= key
        print(n // result)
    elif numbersKey == 1 and sum(arr.values()) >= 6:
        print('YES')
        for key in arr:
            print(key, int(math.pow(key, 2)), int(n // math.pow(key, 3)))
    else:
        print('NO')