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:
# lines = [int(line) for line in open('CodeForces_1294C.in', 'r').readlines()[1:]]
lines = [int(line) for line in [*open(0)][1:]]

for n in lines:
    sol = []
    d = 2
    done = False
    while d * d <= n:
        if n % d == 0:
            n //= d
            sol.append(d)
            if len(sol) == 2:
                done = True
                if n not in sol:
                    sol.append(n)
                    print("YES")
                    print(' '.join(map(str, sol)))
                else:
                    print("NO")
                break
        d += 1
    if not done:
        print("NO")