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:
# cook your dish here
def factor(n):
    a=[]
    for x in range(2,int(n**.5)+1):
        if n%x==0 and (x!=n//x):
            a.append([x,n//x])
    return a
t=int(input())
while(t):
    t=t-1
    found=False
    n=int(input())
    for f in range(2,int(n**.5)+1):
        if n%f==0:
            j=factor(n//f)
            for x in j:
                if x[0]!=f and x[1]!=f:
                    print("YES")
                    print(f,x[0],x[1])
                    found=True
                    break
        if found:
            break
    if found==False:
        print("NO")