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:
import math
t = int(input())
for i in range(t):
    n = int(input())
    q = int( math.sqrt(n))
    l = set()
    for j in range(2, q + 1):
        if n % j == 0:
            l.add(j)
    if len(l) < 2:
        print('NO')
    else:
        l = sorted(list(l))
        res = False
        for k  in range(len(l) - 1):
            for p in range(k + 1, len(l)):
                a = l[k]
                b = l[p]
                c = (n // a )// b
                if a * b * c == n and b != c and a != c:
                    res  = True
                    print("YES")
                    print(str(a) + ' ' + str(b) + ' ' + str(c)) 
                    break
            if res:
                break
        if not res:
            print('NO')