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
from collections import defaultdict
def divisors(n, ans):
    i = 2
    while i <= math.sqrt(n):

        if (n % i == 0):
            if (n / i == i):
                ans.append(i)
            else:
                ans.append(i)
                ans.append(n // i)
        i = i + 1

for _ in range(int(input())):
    n = int(input())
    d1 = []
    # d2 = []
    divisors(n, d1)
    rec = defaultdict(int)
    for i in d1:
        rec[i] = 1
    flag = 0

    for i in d1:
        d2 = []
        divisors(n//i, d2)
        for j in d2:
            if rec.get(j, 0) != 0 and rec.get((n//i)//j, 0) != 0 and (n//i)//j != j and (n//i)//j != i and i != j:
                flag = 1
                print('YES')
                print(i, j, (n//i)//j)
                break
        if flag == 1:
            break
    if flag == 0:
        print('NO')