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


def calc(n: int):
    myStack: list = [n]

    for i in range(2, int(math.sqrt(myStack[-1])) + 1):
        x, rem = divmod(myStack[-1], i)
        if rem == 0:
            myStack.pop()
            myStack.append(i)
            myStack.append(x)
            break
    else:
        print('NO')
        return

    for i in range(2, int(math.sqrt(myStack[-1])) + 1):
        x, rem = divmod(myStack[-1], i)
        if rem == 0 and i not in myStack and x not in myStack:
            myStack.pop()
            myStack.append(i)
            myStack.append(x)
            break
    else:
        print('NO')
        return

    if len(set(myStack)) == 3:
        if (myStack[0] * myStack[1] * myStack[2]) == n:
            print('YES')
            print('{0} {1} {2}'.format(myStack[0], myStack[1], myStack[2]))
        else:
            print('NO')
    else:
        print('NO')


def main():
    for _ in range(int(input())):
        calc(int(input()))


if __name__ == '__main__':
    main()