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:
for j in range(int(input())):
    n=int(input())
    flag = False
    for i in range(2,int(n**(1/3))+1):
        if n%i==0:
            z=n//i
            for k in range(i+1,int(z**0.5)+1):
                if z%k==0 and k*k!=z:
                    flag=True
                    print("YES")
                    print(i,k,z//k)
                    break
        if flag==True:
            break
    if flag==False:
        print("NO")