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 i in range(t):
    n = int(input())
    Ans = []
    d = 2
    while d * d <= n:
        if n % d == 0:
            Ans.append(d)
            break
        else:
            d += 1
    if len(Ans) == 0:
        Ans.append(n)
    n //= Ans[-1]
    while d * d <= n:
        if n % d == 0 and Ans[-1] != d:
            Ans.append(d)
            break
        else:
            d += 1
    if len(Ans) == 1:
        Ans.append(1)
    if len(Ans) >= 2:
        c = n // Ans[-1]
        if c >= 2 and Ans[0] >= 2 and Ans[1] >= 2 and c != Ans[-1] != Ans[-2]:
            Ans.append(c)
            print('YES')
            print(*Ans)
        else:
            print('NO')
    else:
        print('NO')