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:
kl = int(input())
for l in range(kl):
    pr = 0
    n = int(input())
    t = int(n ** 0.5)
    a = []
    for i in range(2, t + 1):
        if n % i == 0:
            a += [i]
            n = n // i
        if len(a) == 2:
            pr = 1
            break
    if pr and a[1] < n:
        print('YES')
        print(a[0], a[1], n)

    else:
        print('NO')