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 prime_divisors(n):
    res = []
    d = 2
    while d * d <= n:
        if n % d == 0:
            if len(res) > 0 and res[-1][0] == d:
                res[-1][1] = res[-1][1] + 1
            else:
                res.append([d, 1])
            n = n // d
        else:
            d = d + 1
    if n > 1:
        if len(res) > 0 and res[-1][0] == n:
            res[-1][1] = res[-1][1] + 1
        else:
            res.append([n, 1])

    return res


t = int(input())
for i in range(t):
    a = int(input())
    pds = prime_divisors(a)
    first_divisor = pds[0][0]
    if len(pds) >= 3:
        second_divisor = pds[1][0]
        ans = [first_divisor, second_divisor, a // (first_divisor * second_divisor)]
        print("YES")
        print(*ans)
    elif len(pds) == 1:
        if pds[0][1] <= 5:
            print("NO")
        else:
            print("YES")
            print(first_divisor, first_divisor * first_divisor, a // (first_divisor * first_divisor * first_divisor))
    else:
        if pds[0][1] + pds[1][1] >= 4:
            second_divisor = pds[1][0]
            print("YES")
            print(first_divisor, second_divisor, a // (first_divisor * second_divisor))
        else:
            print("NO")