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 find_div(x, j):
    for i in range(2, int(x**.5)+1):
        if x % i == 0 and i != j and x//i !=j and i != x//i:
            return True, i, x//i
    return False, -1, -1

t = int(input())
for _ in range(t):
    n = int(input())
    for i in range(2, int(n**.5)+1):
        if n % i == 0:
            ok, a, b = find_div(n//i, i)
            if ok: 
                print('YES')
                print(i, a, b)
                break
    else:
        print('NO')