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:
t = int(input())
for kek in range(t):
    n = int(input())
    i = 2
    s = list()
    while i < n ** (1 / 2) + 1:
        if n % i == 0:
            s.append(i)
            n //= i
        else:
            i += 1
    if n != 1:
        s.append(n)
    a = list()
    a.append(s[0])
    x = 1

    for i in range(1, len(s)):
        x *= s[i]
        if x not in a:
            a.append(x)
            x = 1
        else:
            continue
    a[-1] *= x

    if len(a) >= 3:
        x = 1
        for i in range(2, len(a)):
            x *= a[i]
        print('YES')
        print(a[0], a[1], x)
    else:
        print('NO')