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:
import sys

t = int(sys.stdin.readline().rstrip())
for _ in range(t):
    n = int(sys.stdin.readline().rstrip())
    i = 2
    sol = []
    while i<=n**(1/2):
        if n%i == 0:
            n = n//i
            sol.append(str(i))
        i+=1
        if len(sol) == 2:
            if str(n) not in sol and n != 1:
                sol.append(str(n))
                break

    if len(sol) == 3:
        print('YES')
        print(' '.join(sol))
    else:
        print('NO')