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
def fact(k):
    for i in range(2,(int(sqrt(k)+1))):
        if k%i == 0:
            if k//i != i:
                f = k//i
                return f,i
    return 0,0

def main():
    t = int(input())
    for __ in range(t):

        n  = int(input())
        flag = False
        for i in range(2,(int(sqrt(n)+1))):
            if n%i == 0:
                if n//i != i:
                    f = n//i
                    a,b = fact(i)
                    c,d = fact(f)

                    if a != f and b != f and(a != 0):
                        print("YES")
                        print(a,b,f)
                        flag = True
                        break
                    elif c != i and d != i and(d != 0):
                        print("YES")
                        print(c,d,i)
                        flag = True
                        break
        if not flag:
            print("NO")

if __name__ == '__main__':
    main()