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 as mt
n = int(input())
i = 0
while i < n:
    case = int(input())
    n1 = case
    a, b, c = 1, 1, 1
    divisor = []
    for p in range(2, mt.ceil(mt.sqrt(case + 1))):
        if len(divisor) == 2:
            divisor.append(int(n1 / (divisor[0] * divisor[1])))
            break
        elif case % p == 0:
            divisor.append(p)
            case /= p
    try:
        a, b, c = tuple(divisor)
    except ValueError:
        a, b, c = 1, 1, 1
    if a == 1 or b == 1 or c == 1 or a == c or a == b or b == c:
        ans = False
    else:
        ans = True
    if ans:
        print("YES")
        print(a, b, c)
    else:
        print("NO")
    i += 1