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 #2 2 2 3| 2 2 3
def fac(x):
    i=2
    a = []
    while i*i<=x:
        if x%i==0:
            a.append(i)
            x//=i
        else: i+=1
    if x>1:
        a.append(x)
    return a
def res(x):
    f = fac(x)
    if len(f)<=2 or len(set(f))==1 and len(f)<6 or len(set(f))==2 and len(f)<=3:
        print("NO")
        return 0
    a = f[0]
    l = 1
    r = len(f)-1
    s = 1
    for i in f[l:r+1]:
        s*=i
    b = s
    h = 31
    c = 1
    while h>0:
        if c!=1 and c!=a and c!=b: break
        else:
            c=int(c*(f[r]))
            b= int(b/(f[r]))
            r-=1
            if l == r: break
        h-=1
    print("YES")
    b, c = min(b,c),max(b,c)
    print(a,b,c)

n = int(input())
while n>0:
    x = int(input())
    res(x)
    n-=1