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:
N = int(input())

for _ in range(N):
    x = int(input())
    d = 2
    ans = []
    for steps in range(2):
        if d > x:
            break
        while d * d <= x:
            if x % d == 0:
                ans.append(d)
                x //= d
                d += 1
                break
            d += 1
    if len(ans) == 2 and x >= d:
        print('YES')
        print(*(ans + [x]))
    else:
        print('NO')