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 i in range(t):
    N = int(input())
    answer = []
    F = 0
    for i in range(2,int(N**0.5)+1):
        if N%i == 0:
            X = i
            Z = N//i
            for j in range(2,int(Z**0.5)+1):
                if Z%j==0:
                    ANS1=Z//j
                    if ANS1!=j and ANS1!=X and j!=X:
                        print("YES")
                        print(ANS1,j,X)
                        F=1
                        break
            if F==1:
                break
    if F==0:
        print("NO")