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
t = int(input())
for test in range(t):
    n = int(input())
    k = int(sqrt(n))
    a = 0
    b = 0
    c = 0
    for j in range(2,k+1):
        if n %j == 0:
            n = n//j
            a = j
            break
    k = int(sqrt(n))
    for j in range(2,k+1):
        if n %j == 0 and not(j==a) and not(a == n//j):
            n = n//j
            b = j
            break
    c = n
    if c > 1 and a> 0 and b > 0 and not(c==b):
        print('YES')
        print(a,b,c)
    else:
        print('NO')