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

def divisorGenerator(n):
    large_divisors = []
    for i in range(1, int(math.sqrt(n) + 1)):
        if n % i == 0:
            yield i
            if i*i != n:
                large_divisors.append(int(n / i))
    for divisor in reversed(large_divisors):
        yield divisor

n = int(input())
for x in range(n):
    a = int(input())
    t = (list(divisorGenerator(a)))
    t.pop(-1)
    t.pop(0)
    b1 = False
    b2 = False
    if len(t)<=2:
        print('NO')
        continue
    for z in range(0, len(t)-2):
        for zz in range(z+1, len(t)-1):
            for zzz in range(zz+1, len(t)):
                if t[z]*t[zz]*t[zzz] == a:
                    print('YES')
                    print(t[z], t[zz], t[zzz])
                    b1 = True
                    break
            if b1 == True:
                b2 = True
                break
        if b2 == True:
            break
    if b1 == False and b2 == False:
        print('NO')