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_factors(n):
    i = 2
    factors = []
    while i * i <= n:
        if n % i:
            i += 1
        else:
            n //= i
            factors.append(i)
    if n > 1:
        factors.append(n)
    return factors


m = int(input())
for i in range(m):
    n = int(input())
    if len(prime_factors(n)) < 3:
        print("NO")
    else:
        a = prime_factors(n)[0]
        if prime_factors(n)[0] == prime_factors(n)[1]:
            b = prime_factors(n)[1] * prime_factors(n)[2]
            if len(prime_factors(n)) == 3:
                print("NO")
            else:
                c = 1
                for el in prime_factors(n)[3:]:
                    c *= el
                if a != b != c and a != c:
                    print("YES")
                    print(a, b, c)
                else:
                    print("NO")
        else:
            b = prime_factors(n)[1]
            c = 1
            for el in prime_factors(n)[2:]:
                c *= el
            if a != b != c and a != c:
                print("YES")
                print(a, b, c)
            else:
                print("NO")