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 sys import stdin


inp = stdin.readline

t = int(inp())

for i in range(t):
    n = int(inp())
    a = b = 0
    for j in range(2, int(n**0.5) + 1):
        if n % j == 0:
            if a == 0:
                a = j
                n //= j
            elif b == 0:
                b = j
                n//=j
                break
    if a!= 0 and b != 0 and n != a and n!= b:
        print("YES")
        print(a,b,n)
    else:
        print("NO")