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 a in range(t):
    n = ori = int(input())
    num = []
    for b in range(2,int(ori**0.5)+1):
        # print(n)
        if n % b == 0:
            num.append(b)
            n = n//b
            if len(num) == 2:
                if n != 1:
                    num.append(n)
                break
    num = list(set(num))
    if len(num) == 3:
        print("YES")
        print(" ".join(map(str, num)))
    else:
        print("NO")