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:
def product(n):
    a = int(min_divisor(2,n))
    if a==n:
        return False
    else:
        b = int(min_divisor(a+1,n/a))
        if b==a or b==1:
            return False
        else:
            c = int(n/(a*b))
            if c==a or c == b or c==1:
                return False
            else:
                return (a, b, c)
def min_divisor(s,n):
    for i in range(s,int(n**0.5)+1):
        if n % i == 0:
            return i
    else:
        return n

t = int(input())
for i in range(t):
    n = int(input())
    ans = product(n)
    if ans:
        print("YES")
        print(*list(ans))
    else:
        print("NO")