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:
from math import sqrt, floor

t = int(input())
for _ in range(t):
    n = int(input())
    if n < 24:
        print("NO")
    else:
        m = floor(sqrt(n)) + 1
        d = 0
        divs = []
        for i in range(2, m):
            if n % i == 0:
                d += 1
                divs.append(i)
                n //= i
                break
        if d == 0:
            print("NO")
        else:
            m = floor(sqrt(n)) + 1
            for i in range(divs[0]+1, m):
                if n % i == 0:
                    d += 1
                    divs.append(i)
                    n //= i
                    break
            if d == 2:
                if n in divs:
                    print("NO")
                else:
                    divs.append(n)
                    ans = map(str, divs)
                    print("YES")
                    print(' '.join(ans))
            else:
                print("NO")