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:

c = int(input())

def handleCase(n):
    cap = int(n ** 0.40) + 1
    for i in range(2, cap):
        if n % i == 0:
            q = n // i
            for j in range(i + 1, int(q ** 0.5) + 1):
                if q % j == 0 and not q == j * j:
                    return str(i) + ' ' + str(j) + ' ' + str(n // i // j)

for _ in range(c):
    n = int(input())
    ans = handleCase(n)
    if ans:
        print('YES')
        print(ans)
    else:
        print('NO')