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:
for _ in range(int(input())):
    num = int(input())
    list_of_nums = [1]
    for i in range(2, int(pow(num, .5)+1)):
        if num % i == 0:
            num = num // i
            list_of_nums.append(i)
            break
    # print(list_of_nums)
    for i in range(2, int(pow(num, .5))+1):
        if num % i == 0 and i not in list_of_nums:
            num //= i
            list_of_nums.append(i)
            break
    # print(list_of_nums)
    if num not in list_of_nums and len(list_of_nums) > 2:
        print("YES")
        list_of_nums = [str(x) for x in list_of_nums]
        print(num, ' '.join(list_of_nums[1:]))
    else:
        print("NO")