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:
a, i = int(input()), 0
def pro(a):
    p, i = 0, 2
    while i * i <= a:
        if a % i == 0:
            p = i
            break
        i = i + 1
    return p
def f1(k, ak, a):
    i, t = 2, 0
    while i * i <= ak:
        if a % i == 0:
            if ak // i != i and i != k and (ak // i) * i * k == a:
                print("YES")
                print(int(ak / i), int(i), int(k))
                t = 1
                break
        i = i + 1
    if t == 0:
        print("NO")
    return 0
def ff(a):
    k = pro(a)
    if k == 0:
        print("NO")
    else:
        f1(k, a / k, a)
    return 0
while i != a:
    x = int(input())
    ff(x)
    i = i + 1