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
def factorize(n):
    i = 2
    s = int(math.sqrt(n))
    f = dict()
    while n > 1:
        if i > s:
            # print(i,s,n,f)
            f[i] = 1
            return f
        if n % i == 0:
            f[i] = f.get(i, 0) + 1
            n //= i
        else:
            i += 1
    return f


t = int(input())
for _ in range(t):
    n = int(input())
    f = factorize(n)
    if len(f) == 1:
        x = list(f.keys())[0]
        if f[x] >= 6:
            print("YES")
            print(int(x), int(x**2), int(x**(f[x]-3)))
        else:
            print("NO")
    elif len(f) == 2:
        x = list(f.keys())
        x1, x2 = x[0],x[1]
        if (f[x1] == 2 and f[x2] == 2):
            print("YES")
            print(int(x1), int(x2), int(x1*x2))
        elif f[x1] >= 3:
            print("YES")
            print(int(x1), int(x1*x1), int(n//(x1**3)))
        elif f[x2] >= 3:
            print("YES")
            print(int(x2), int(x2*x2), int(int(n//(x2**3))))
        else:
            print("NO")
    else:
        print("YES")
        x = list(f.keys())
        print(int(x[0]), int(x[1]), (n//(x[0]*x[1])))