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:
import math
for _ in range(int(input())):
    n = int(input())
    a = -99
    t = 0
    if(n < 24):
        print("NO")
    else:    
        for i in range(2, (int)(math.sqrt(n)) + 1):
            if(n%i == 0):
                if(a > 0):
                    if(n%(i*a) == 0):
                        if(a != i) and (i != (n//(i*a))) and (n//(i*a) > 2) and (a != (n//(i*a))):
                            print("YES")
                            print(a,end=' ')
                            print(i, end=' ')
                            print((n//(i*a)))
                            t = 1
                            break
                else:
                    a = i
                    if(n%(i*a) == 0):
                        if(a != i) and (i != (n//(i*a))) and (n//(i*a) > 2) and (a != (n//(i*a))):
                            print("YES")
                            print(a,end=' ')
                            print(i, end=' ')
                            print((n//(i*a)))
                            t = 1
                            break
        if(t == 0):
            print("NO")