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 sys
input = sys.stdin.readline

def make_divisors(n):
    divisors = []
    for i in range(1, int(n**0.5)+1):
        if n % i == 0:
            divisors.append(i)
            if i != n // i:
                divisors.append(n//i)

    # divisors.sort()
    return divisors


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

        d = make_divisors(N)
        if len(d) <= 2:
            print("NO")
            continue

        fl = False
        for i in d:
            if i == 1 or i == N:
                continue
            f = make_divisors(N // i)
            if len(f) <= 2:
                continue
            for j in f:
                if j == 1 or j == (N // i):
                    continue
                k = (N // i) // j
                if k != i and j != i and k != j:
                    print("YES")
                    print(i, j, k)
                    fl = True
                    break
            if fl:
                break
        if not fl:
            print("NO")


if __name__ == '__main__':
    main()