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 countDivisors(n) : 
    cnt = 0
    for i in range(1, (int)(math.sqrt(n)) + 1) : 
        if (n % i == 0) : 
              
            # If divisors are equal, 
            # count only one 
            if (n / i == i) : 
                cnt = cnt + 1
            else : # Otherwise count both 
                cnt = cnt + 2
                  
    return cnt
t=int(input())
for i in range(t):
    n=int(input())
    x=0
    w=1
    for j in range(2,int(math.sqrt(n))+1):
        if(n%j==0):
            r=countDivisors(n//j)
            if(r>3):
                
                for k in range(2,int(math.sqrt(n//j))+1):
                    if((n//j)%k==0 and j!=k and k!=(n//j)//k and j!=(n//j)//k):
                        print("YES")
                        print(j,k,(n//j)//k)
                        w=0
                    if(w==0):
                        break
        if(w==0):
            break
    if(w==1):
        print("NO")