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 solveOne(n):
    ret = []
    d = 2
    while d * d < n and len(ret) < 3:
        if n % d == 0:
            ret.append(d)
            n //= d
            dd = 2
            while dd * dd < n:
                if n % dd == 0 and dd not in ret and n // dd not in ret:
                    ret.extend((dd, n // dd))
                    break
                dd += 1
        d += 1
    return 'YES\n%s' % ' '.join(map(str, ret)) if len(ret) == 3 else 'NO'


for _ in range(int(input())):
    print(solveOne(int(input())))