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 
import math
t = int(input())
for i in range(t):
    n = int(input())
    f = 1
    for a in range(2, int(math.sqrt(n)) + 1):
        if f and n % a == 0:
            curn = n // a
            for b in range(2, int(math.sqrt(curn)) + 1):
                if f and b != a and curn % b == 0:
                    c = curn // b
                    if c != b and c != a:
                        print('YES')
                        print(a, b, c)
                        f = 0
    if f:
        print('NO')