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 x in range(int(input())):
    n = int(input())
    a = 1
    for i in range(2, int(n ** 0.5) + 2):
        if n % i == 0:
            a = i
            n /= i
            break
    if a != 1:
        b = 1
        for i in range(a + 1, int(n ** 0.5) + 2):
            if n % i == 0:
                if n // i != a and n // i != i:
                    b = i
                    n /= i
                    break
        if b != 1:
            if n != 1:
                print('YES')
                print(a, b, int(n))
            else:
                print('NO')
        else:
            print('NO')

    else:
        print('NO')