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

for _ in range(int(input())):
    t = n = int(input())
    dels = []
    sq = int(math.sqrt(n))
    d = 2
    while d <= sq:
        if n % d != 0:
            d += 1
        else:
            dels.append(d)
            n //= d
            sq = int(math.sqrt(n))

    dels.append(n)
    a = dels[0]
    b = 1
    i = 1
    while i < len(dels) and b <= a:
        b *= dels[i]
        i += 1

    a, b, c = sorted([a, b, t // (a * b)])
    # print(dels, '\n', a, b, c)
    if (a > 1) and (a < b < c):
        print('YES')
        print(a, b, t // (a * b))
    else:
        print('NO')