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 solve(unique,arr):
    if len(unique) >= 3 and len(arr) >= 3:
        a,b = unique[0],unique[1]
        c = n//(a*b)
        return [a,b,c]
    elif len(unique) == 1 and len(arr) >= 6:
        a,b = unique[0],pow(unique[0], 2)
        c = n // pow(a, 3)
        return [a,b,c]
    elif len(unique) == 2 and len(arr) >= 4:
        a,b = unique[0],unique[1]
        c = n // (a*b)
        return [a,b,c]
    else:
        return "NO"

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

for _ in range(int(input())):
    n = int(input())
    arr = sieve(n)
    unique = list(set(arr))
    f = solve(unique,arr)
    if f=='NO':
        print("NO")
    else:
        print("YES")
        print(*f)