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 find_factors(n):
    l = []
    while n % 2 == 0:
        l.append(2)
        n //= 2
    for i in range(3,int(math.sqrt(n)+1),2):
        while n % i == 0:
            l.append(i)
            n //= i
    if n > 2:
        l.append(n)
    return l


for _ in range(int(input())):
    n = int(input())
    k0 = find_factors(n)
    k1 = list(dict.fromkeys(k0))
    # print(k0)
    # print(k1)
    if len(k1) == 1:
        if len(k0) <= 5:
            print("NO")

        else:
            print('YES')
            pro = 1
            for i in range(3,len(k0)):
                pro *= k0[i]
            print(k0[0],k0[1]*k0[2],pro)

    elif len(k1) == 2:
        if len(k0) <= 3:
            print("NO")

        else:
            pro = 1
            print("YES")
            for i in range(1,len(k0)-1):
                pro *= k0[i]
            print(k0[0],k0[-1],pro)

    elif len(k1) == 3:
        b = [1,1,1]
        print("YES")
        for i in range(len(k0)):
            if k0[i] == k1[0]:
                b[0] *= k0[i]
            elif k0[i] == k1[1]:
                b[1] *= k0[i]
            else:
                b[2] *= k0[i]
        print(*b)

    else:
        m = k1[0]
        n = k1[1]
        k0.remove(m)
        k0.remove(n)
        pro = 1
        print("YES")
        for i in range(len(k0)):
            pro *= k0[i]
        print(m,n,pro)