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
t=int(input())
def f(a):
    b=2
    a=int(a)
    fac=[]
    c=math.sqrt(a)
    while b<=c and a>1:
        if a%b==0:
            while a%b==0:
                fac.append(b)
                a/=b
            b+=1
        else:
            b+=1
    if a!=1:
        fac.append(a)
    return fac

for i in range(t):
    n=int(input())
    list=f(n)
    list2=[]
    list2.clear()
    while list:
        i=list[0]
        b=list.count(i)
        list2.append([i,b])
        for j in range(b):
            list.remove(i)
    c=len(list2)
    if c>=3:
        print("YES")
        print(list2[0][0],list2[1][0],int(n/list2[0][0]/list2[1][0]))
    elif c==1:
        if(list2[0][1]>=6):
            print("YES")
            print(list2[0][0],list2[0][0]*list2[0][0],int(n/list2[0][0]/list2[0][0]/list2[0][0]))
        else:
            print("NO")
    elif c==0:
        print("NO")
    else:
        if(list2[0][1]>=2 and list2[1][1]>=2):
            print("YES")
            print(list2[0][0],list2[1][0],int(n/list2[0][0]/list2[1][0]))
        elif list2[0][1]>=3:
            print("YES")
            print(list2[0][0],int(list2[1][0]),int(n/list2[0][0]/list2[1][0]))
        elif list2[1][1]>=3:
            print("YES")
            print(list2[0][0], list2[1][0],int(n/list2[0][0]/list2[1][0]))
        else:
            print("NO")