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
from math import sqrt
def primeFactors(n): 
    a=[]
    # Print the number of two's that divide n 
    while n % 2 == 0: 
        a.append(2) 
        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: 
            a.append(i) 
            n = n / i 
              
    # Condition if n is a prime 
    # number greater than 2 
    if n > 2: 
        a.append(n)
    return a
t=int(input())
for _ in range(t):
    n=int(input())
    s=set([])
    x=int(sqrt(n))+2
    for i in range(2,x):
        if n%i==0:
            s.add(i)
            n=n//i
            break
    x=int(sqrt(n))+2
    for i in range(2,x):
        if n%i==0 and i not in s:
            s.add(i)
            s.add(n//i)
            break
    a=list(s)
    if len(a)==3:
        print("YES")
        print(*a)
    else:
        print("NO")


    # a = primeFactors(n)
    # a.sort()
    # s=set([])
    # if len(a)>3:
    #     s.add(a[0])
    #     if a[0]==a[1]:
    #         s.add(a[1]*a[2])
    #         k=1
    #         for i in range(3,len(a)):
    #             k*=a[i]
    #         if k in s:
    #             s=set([])
    #             s.add(a[0])
    #             s.add(a[1]*a[-1])
    #             k=1
    #             for i in range(2,len(a)-1):
    #                 k*=a[i]
    #             if k in s:
    #                 print("NO")
    #                 continue
    #             else:
    #                 s.add(k)
    #                 a=list(s)
    #                 print("YES")
    #                 print(int(a[0]),int(a[1]),int(a[2]))
    #                 continue
    #         else:
    #             s.add(k)
    #             a=list(s)
    #             print("YES")
    #             print(int(a[0]),int(a[1]),int(a[2]))
    #             continue
    #     else:
    #         s.add(a[1])
    #         for i in range(2,len(a)):
    #             k*=a[i]
    #         if k in s:
    #             print("NO")
    #             continue
    #         else:
    #             s.add(k)
    #             a=list(s)
    #             print("YES")
    #             print(int(a[0]),int(a[1]),int(a[2]))  
    #             continue          
    # elif len(a)==3:
    #     temp=list(set(a))
    #     if len(temp)==3:
    #         print("YES")
    #         print(int(a[0]),int(a[1]),int(a[2]))
    # else:
    #     print("NO")