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 product_of_three_numbers():
    num_test = int(input())
    count = 0
    n_list = []
    while count < num_test:
        n_list += [int(input())]
        count += 1

    answer_list = []

    for idx, n in enumerate(n_list):
        if n <= 5:
            answer_list += ["NO"]
            continue
        breakit = False
        for a in range(2, n+1):
            if (a-1)*(a-1) >= n:
                answer_list += ["NO"]
                break
            if n%a == 0:
                divbya = int(n/a)
                if divbya <= a:
                    answer_list += ["NO"]
                    break
                for b in range(a, divbya):
                    if (b-1)*(b-1) >= divbya:
                        answer_list += ["NO"]
                        breakit = True
                        break
                    if divbya%b == 0:
                        if b==a:
                            continue
                        divbyb = int(divbya/b)
                        if divbyb <= b:
                            answer_list += ["NO"]
                            breakit = True
                            break
                        answer_list += ["YES"]
                        answer_list += [str(a)+" "+str(b)+" "+str(divbyb)]
                        breakit = True
                        break

            if breakit:
                break

    for answer in answer_list:
        print(answer)

product_of_three_numbers()