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:
def nonprime(number,start=2):
    from math import sqrt
    for i in range(start,int(sqrt(number))+1):
        if number%i==0:
            return [True,i]
    return [False]
testcases=int(input())
for k in range(testcases):
    numbertobetested=int(input())
    initial=nonprime(numbertobetested)
    if initial[0]:
        k=nonprime(numbertobetested//initial[1],start=initial[1]+1)
        if k[0] and (initial[1]!=k[1] and initial[1]!=((numbertobetested//initial[1])//k[1]) and k[1]!=((numbertobetested//initial[1])//k[1])):
            print("YES")
            print(str(initial[1])+" "+str(k[1])+" "+str(((numbertobetested//initial[1])//k[1])))
        else:
            print("NO")
    else:
        print("NO")