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
for _ in range(int(input())):
    n = int(input())
    def prime(n):
        primes = {2:0}
        while n % 2 == 0:
            primes[2] += 1
            n = n // 2
        for i in range(3, int(math.sqrt(n)+1), 2):
            while n % i == 0:
                if i in primes:
                    primes[i] += 1
                else:
                    primes[i] = 1
                n = n // i
        if n > 2:
            if n in primes:
                primes[n] += 1
            else:
                primes[n] = 1
        return primes
    def prod(l):
        p = 1
        for x in l:
            p *= x
        return p
    primes = prime(n)
    # print(primes)
    ar = []
    keys = sorted(primes.keys())
    for key in keys:
        ar.extend([key]*primes[key])
    # print(ar)
    if len(ar) < 3:
        print('NO')
    else:
        a = ar[0]
        i = 1
        b = ar[1]
        if ar[0] == ar[1]:
            b *= ar[2]
            i += 1
        c = prod(ar[i+1:])
        if i == len(ar) - 1 or b == c or len(set([a, b, c])) < 3:
            print('NO')
        else:
            print('YES')
            print(a, b, c)