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 floor, sqrt
try: 
    long
except NameError: 
    long = int
 
def fac(n):
    step = lambda x: 1 + (x<<2) - ((x>>1)<<1)
    maxq = long(floor(sqrt(n)))
    d = 1
    q = 2 if n % 2 == 0 else 3 
    while q <= maxq and n % q != 0:
        q = step(d)
        d += 1
    return [q] + fac(n // q) if q <= maxq else [n]
for _ in range(int(input())):
    n=int(input())
    l=fac(n)
    l.sort()
    k=len(l)
    if k>3:
        if len(set([l[0],l[1]*l[2],n//(l[0]*l[1]*l[2])]))==3:
            print("YES")
            print(l[0],l[1]*l[2],n//(l[0]*l[1]*l[2]))
        elif len(set([l[0],l[1]*l[-1],n//(l[0]*l[1]*l[-1])]))==3:
            print("YES")
            print(l[0],l[1]*l[-1],n//(l[0]*l[1]*l[-1]))
        elif len(set([l[1],l[0]*l[2],n//(l[0]*l[1]*l[2])]))==3:
            print("YES")
            print(l[1],l[0]*l[2],n//(l[0]*l[1]*l[2]))
        elif len(set([l[2],l[0]*l[1],n//(l[0]*l[1]*l[2])]))==3:
            print("YES")
            print(l[2],l[0]*l[1],n//(l[0]*l[1]*l[2]))
        else:
            print("NO")
    elif k==3 and len(set(l))==3:
        print("YES")
        print(l[0],l[1],l[2])
    else:
        print("NO")