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())
if t<=100:
    while t>0:
        l=list()
        n = int(input())
        x = int(2)
        y = int(2)
        z = int(2)
        for i in range(2,round(n**0.5)+1):
            if n%i == 0 and not(i in l):
                n=n//i
                l.append(i)
                break
        for i in range(2, round(n ** 0.5)+1):
            if n%i == 0 and not (i in l):
                n = n // i
                l.append(i)
                break
        if not(n in l) and n>1 and len(l)==2:
            print('YES')
            print(l[0],l[1],n)
        else :
            print('NO')
        t -= 1