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())

    sqn = int(n**(1/2))+10
    ans = []
    flag = False
    for i in range(2,sqn):
        if n%i==0:
            ans.append(i)
            n//=i
            if len(ans)==2:
                if n==ans[1] or n==ans[0] or n==1:
                    print("NO")
                else:
                    print("YES")
                    print(*ans,n)
                flag = True
                break
    if not flag:
        print("NO")