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 sys
#sys.stdin = open("division.in","r")
#sys.stdout = open("division.out","w")
t = int(input())
for i in range(t):
    n = int(input())
    i = 2
    flag = 0
    while(i ** 2 <= n):
        if n % i == 0:
            a = i
            j = 2
            while(j ** 2 <= (n // a)):
                if (n // a) % j == 0:
                    b = (n // a) // j
                    c = (n // a) // b
                    if a != b and a != c and b != c:
                        flag = 1
                        break
                j += 1
        i += 1
        if flag:
            print("YES")
            print(a,b,c)
            break
    if not flag:
        print("NO")