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 PYTHON):

Solution:
def find_multipliers(n):
    if n < 8:
        return None
    
    a = b = c = None
    for i in range(2, int(n**0.5 + 1)):
        if n % i == 0:
            a = i
            break
    if a is None:
        return None
    n /= a
    for i in range(2, int(n**0.5 + 1)):
        if (i != a) and (n % i == 0):
            b = i
            break
    if b is None:
        return None
    c = n / b
    if (c == a) or (c == b):
        return None
    return a, b, c

t = int(input())

for _ in range(t):
    n = int(input())
    result = find_multipliers(n)
    if result is None:
        print("NO")
    else:
        print("YES")
        print(" ".join(map(str, result)))