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 three_multiply(n):
    a, b, c = 0, 0, 0
    for i in range(2, n // 2):
        if i * i > n:
            break
        if n % i == 0:
            a = i
            n = n // i
            break
    for i in range(a + 1, n // 2):
        if i * i > n:
            break
        if n % i == 0:
            b = i
            if n // i > b:
                c = n // i
            break
    if a and b and c:
        print("YES")
        print(a, b, c)
    else:
        print("NO")


t = int(input())
X = []
x = [X.append(int(input())) for i in range(t)]
for x in X:
    three_multiply(x)