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 math
t = int(input())


def solve(n):
    f = []
    while (n % 2 == 0):
        f.append(2)
        n = n / 2
    R = int(math.sqrt(n))
    for e in range(3, R + 1, 2):
        while (n % e == 0):
            f.append(e)
            n = n / e
    if n != 1.0:
        f.append(int(n))
    return f


while t > 0:
    t -= 1
    n = int(input())
    factors = solve(n)
    # print(factors)
    if len(factors) <= 2:
        print("NO")
    else:
        factors.sort()
        a = factors[0]
        pos = 1
        b = 1

        while b <= a:
            b = b * factors[pos]
            pos += 1

        # print(a, b, pos)
        c = 1
        if pos == (len(factors)):
            print("NO")
            continue
        for e in range(pos, len(factors)):
            c = c * factors[e]

        if a != b and b != c and a != c:
            print("YES")
            print("{} {} {}".format(a, b, c))
        else:
            print("NO")