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(n):
    i = 2
    f = []
    s = n
    while i*i <= n:
        while s % i == 0:
            s //= i
            f.append(i)
        i += 1
    else:
        if s > 1:
            f.append(s)
    return f


def solve():
    f = factors(n)
    s = set()
    i = 0
    x = 1
    for i in f:
        if i not in s:
            s.add(i)
            if len(s) == 2: break
        else:
            x *= i
            if x != 1 and x not in s:
                s.add(x)
                if len(s) == 2: break
                x = 1

    ss = list(s)
    r = n // (ss[0]*ss[1]) if len(ss) == 2 else 1
    if len(s) == 2 and r != 1 and r != ss[0] and r != ss[1]:
        s.add(r)

    if len(s) >= 3:
        print("YES")
        print(' '.join(map(str, list(s)[:3])))
    else:
        print("NO")
     

def main():
    global n
    for _ in range(int(input())):
        n = int(input())
        solve()


main()