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 prf(x):
    a = []
    b = 1
    n = 2
    m = int(math.sqrt(x))
    # print(m)
    while n <= m:
        if x%n == 0:
            if not(n in a): a.append(n)
            elif not(n*b in a):
                a.append(n*b)
                b = 1
            else: b *= n
            x //= n
        else:
            if n == 2: n += 1
            else: n += 2
        # print(a, b, x, n)
        if len(a) == 2 and not(x*b in a) and x*b>1:
            a.append(x*b)
            return a
        elif len(a) == 3: return a
        elif len(a) == 2:
            return 'NO'
        
    return 'NO'

n = int(input())
for i in range(n):
    x = int(input())
    re = prf(x)
    if type(re) == type('NO'): print(re)
    else:
        print('YES')
        print(*sorted(re))