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 factors(x):
    result = []
    i = 1
    while i*i <= x:
        if x % i == 0:
            result.append(i)
            if x//i != i: #
                result.append(x//i)
        i += 1
    return(result)
for _ in range(int(input())):
    n = int(input())
    lst = sorted(factors(n))
    a = lst[1]
    x = n//a
    lst2 = sorted(factors(x))
    if len(lst2) <= 2:
        b = -1
    elif lst2[1] != a:
        b = lst2[1]
    elif lst2[1] == a and len(lst2) > 2:
        b = lst2[2]

    yo = a*b
    res = n//yo
    if res != a and res!= b and res != 1 and b > 1:
        print("YES")
        print(a,b,res)
    else:
        print("NO")
    #print(lst2)