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:
t=int(input())

for i in range(t):
    a,b,c,j=1,1,1,0
    flag=1
    num = int(input())
    for j in range(2,int((num)**0.5)):
        if num%j==0:
            a=j
            #print(a)
            break
    num=num//a    
    for k in range(j+1,num+1):
        if k >(num**0.5):
            break
        if num%k==0:
            b=k
            #print(b)
            break
    if(num%(b)==0 and b!=int(num/(b)) and a!=int(num/(b))):
        c=int(num/(b))
        #print(c)
        flag=0
    if a!=1 and b!=1 and c!=1:
        print("YES")
        print(("{0:} {1:} {2:}").format(a,b,c))
        #print(a)
    else:
        print("NO")