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 sys import stdin

def Prime(d, n):
    if n%d == 0:
        return d
    while d * d <= n:
        if n % d == 0:
            return d
        d= d + 1
    return 0

for _ in range(int(stdin.readline())):
    n = int(stdin.readline())
    if n < 24 :
        print("NO")
        continue
    ans = []
    count = 0
    cond = True
    d = 2
    while(count<2):
        m = Prime(d, n)
        if m == 0:
            cond = False
            break
        else:
            ans.append(m)
            count += 1
            n = n//m
            d = m+1
    if cond == True:
        if n in ans:
            print("NO")
        else:
            ans.append(n)
            print("YES")
            print(*ans)
    else:
        print("NO")