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
n = int(input())
Resulting_bool_list = []
Resulting_factor_list = []
for i in range(0,n):
    factor_list = []
    temp = []
    num = int(input())
    lim = math.floor(math.sqrt(num))

    for i in range(2,lim+1):
        if num % i == 0:
            factor_list.append(i)

    len_ = len(factor_list)
    if len_ < 3:
        Resulting_bool_list.append('NO')
        Resulting_factor_list.append([])
    else:
        Resulting_bool_list.append('YES')
        temp.append(factor_list[0])
        num = num / factor_list[0]
        for j in range(1,len_):
            if num % factor_list[j] == 0:
                temp.append(factor_list[j])
                temp.append(int(num/factor_list[j]))
                break
        Resulting_factor_list.append(temp)

for i in range(0,n):
    if Resulting_bool_list[i] == 'NO':
        print(Resulting_bool_list[i])

    else:
        print(Resulting_bool_list[i])
        for j in Resulting_factor_list[i]:
            print(j,end=' ')
        print('')