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:


tests = int(input())
for t in range(tests):
    n = int(input())
    initN = n
    i = 2
    a,b = 0,0
    while True:
        if i**2 > initN:
            print("NO")
            break
        if n%i == 0:
            n=n/i
            if a == 0:
                a=i
            elif b==0:
                b=i
        if a > 0 and b > 0 and n > 1 and a != b and b !=n and a!=n:
            print("YES")
            print(str(a)+" "+str(b)+" "+str(int(n)))
            break
        i+=1