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 _ in range(t):
    n =  int(input())
    rt = int(n**.5)
    st = set()
    flag=0
    for i in range(2,rt+1):
        if(n%i==0):
            k = n//i
            v = int(k**.5)
            for j in range(2,v+1):
                if(k%j==0 and i!=j):
                    if(k//j!=i and k//j !=j):
                        print("YES")
                        print(i,j,k//j)
                        flag=1
                        break
        if(flag==1):
            break
    if(flag==0):
        print("NO")