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 wa(a):
    for i in range(2,int(math.sqrt(a)),1):
        if(a%i==0):
            return False
    return True
def ans(a):
    count=0
    f=0
    l=[]
    s=''
    d=int(math.sqrt(a))
    for i in range(2,d+1,1):
        if(a%i==0):
            l.append(i)
            count+=1
            a=a//i
        if(count==2 and l[0]!=a and l[1]!=a):
            l.append(a)
            f=1
            break
    if(f):
        print("YES")
        for i in l:
            print(i,end=' ')
        print()
    else:
        print("NO")
t=int(input())
while(t>0):
    a=int(input())
    if(wa(a)==True):
        print("NO")
    elif(a%10==0):
        x=a//10
        y=2
        z=5
        if(x*z*y==a and x!=y and x!=z and z!=y and x>1 and y>1 and z>1):
            print("YES")
            if(z>x):
                print(y,x,z)
            else:
                print(y,z,x)   
        else:
            print("NO")
    else:
        ans(a)
    
    
    t-=1