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 solve(n):
    a, b, c = None, None, n
    i = 2
    while c >= 2 and i * i <= c:
        if c % i == 0:
            c //= i
            if a is None:
                a = i
            elif c >= 2 and len(set((a, i, c))) == 3:
                return a, i, c
        i += 1
    raise ValueError()

for T in range(int(input())):
    try:
        a, b, c = solve(int(input()))
        print('YES')
        print(a, b, c)
    except ValueError:
        print('NO')