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:
from math import sqrt
t = int(input())
f = ""
for _ in range(t):
    n = int(input())
    m = n
    r = 0
    x = []
    for i in range(2, int(sqrt(n))+1):
        if i>m or r==2:
            break
        else:
            if m%i==0:
                x.append(i)
                m = m//i
                r += 1
    if r==2 and (n//(x[0]*x[1])>x[1]):
        f += "YES\n"
        f += str(x[0]) + " " +str(x[1]) + " " + str(n//(x[0]*x[1]))+"\n"
    else:
        f += "NO\n"
print(f)