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 primeFactors(n,d): 
      
    # Print the number of two's that divide n 
    while n % 2 == 0: 
        try:
            if d[2]>=0:
                d[2]+=1
        except:
            d[2]=1 
        n = n / 2
          
    # n must be odd at this point 
    # so a skip of 2 ( i = i + 2) can be used 
    for i in range(3,int(math.sqrt(n))+1,2): 
          
        # while i divides n , print i ad divide n 
        while n % i== 0: 
            try:
                if d[int(i)]>=0:
                    d[int(i)]+=1
            except:
                d[int(i)]=1
            n = n / i 
              
    # Condition if n is a prime 
    # number greater than 2 
    if n > 2: 
        d[int(n)]=1
    return d
t=int(input())
for r in range(t):
    n=int(input())
    d=primeFactors(n,{})
    if len(d)<3:
        try:
            if d[n]>=0:
                print("NO")
        except:
            if len(d)==1:
                a=1
                for i in d:
                    a=i
                if d[a]<6:
                    print("NO")
                else:
                    print("YES")
                    s=str(a)+" "+str(int(a**2))+" "+str(int(a**(d[a]-3)))
                    print(s)
            else:
                summ=0
                temp=[]
                for i in d:
                    summ+=d[i]
                    temp.append(i)
                if summ<=3:
                    print("NO")
                else:
                    print("YES")
                    a=temp[0]
                    b=temp[1]
                    s=str(int(a))+" "+str(int(b))+" "
                    tempd=(int(a**(d[a]-1)))*(int(b**(d[b]-1)))
                    s+=str(int(tempd))
                    print(s)
                    
    else:
        l=[]
        for i in d:
            l.append(i)
        print("YES")
        s=str(int(l[0]**d[l[0]]))+" "+str(int(l[1]**d[l[1]]))+" "
        temp=1
        for i in range(2,len(l)):
            temp*=(int(l[i]**d[l[i]]))
        s+=str(int(temp))
        print(s)