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:
from math import sqrt, ceil

def primesfrom2to(n):
    """ Returns  a list of primes < n """
    sieve = [True] * (n//2)
    for i in range(3,int(n**0.5)+1,2):
        if sieve[i//2]:
            sieve[i*i//2::i] = [False] * ((n-i*i-1)//(2*i)+1)
            return [2] + [2*i+1 for i in range(1,n//2) if sieve[i]]

primedin105 = primesfrom2to(10 ** 5)

def primedec(n):
    ret = dict()
    if n == 1:
        return ret
    s = ceil(sqrt(n))
    for i in primedin105:
        if s < i:
            return {n : 1}
        if not (n % i):
            d = primedec(n // i)
            ret = d
            try:
                ret[i] += 1
            except Exception:
                ret[i] = 1
            return ret



def solution(n):
    p = primedec(n)
    k = sorted(p.keys())
    a = k[0];
    if p[a] == 1:
        if len(k) == 1:
            print('NO')
            return
        b = k[1]
    elif p[a] == 2:
        if len(k) == 1:
            print('NO')
            return
        b = k[0] * k[1]
    else:
        b = k[0] ** 2

    c = n // (a * b)
    if c == 1 or c == a or c == b:
        print("NO")
        return
    print("YES")
    print(a, b, c)

t = int(input())

for i in range(t):
    solution(int(input()))