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:
for _ in range(int(input())):
    n = int(input())
    if n < 24:
        print("NO")
        continue
    j = -1
    a, b = 0, 0
    for i in range(2, int(n**(1 / 3)) + 1):
        if n % i == 0:
            a = i
            n //= i
            j = i + 1
            break
    if j == -1:
        print("NO")
        continue
    o = -1
    for i in range(j, int(n**(1 / 2)) + 1):
        if n % i == 0:
            b = i
            n //= i
            o = 1
            break
    if o == -1 or n <= b:
        print("NO")
        continue
    print("YES")
    print(a, b, n)