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 compute_problem(n):
    if n < 24:
        print("NO")
    elif n % 10 == 0:
        a = 2
        n_div_10 = int(n/10)
        b = min(5, n_div_10)
        c = max(5, n_div_10)
        if b != c:
            print("YES")
            print(a, b, c, sep=" ")
        else:
            print("NO")
    else:
        result_found = False
        max_a = int(n ** (1. / 3.)) + 1
        for a in range(2, max_a):
            #print("a: ", a)
            if not n % a == 0:
                continue
            max_b = int((int(n/a) + 1)**(1./2.)) + 1
            for b in range(a + 1, max_b):
                #print("b: ", b)
                prod_ab = a * b
                c = int(n/prod_ab)
                #print("c: ", c)
                #print(( (n % prod_ab == 0) , (prod_ab != n) , (c != a) , (c != b)))
                result_found = (n % prod_ab == 0) and (prod_ab != n) and (c != a) and (c != b)
                #print(result_found)
                if result_found:
                    print("YES")
                    print(a, b, c, sep=" ")
                    break
            if result_found:
                break
        if not result_found:
            print("NO")

num_tests = int(input())

for test_num in range(0, num_tests):
    test_case = input()
    if test_case:
        aim_num = int(test_case)
        compute_problem(aim_num)