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 
import math

a = int(input())
for x in range(a):
    a = int(input())
    prime = 2
    count = list()
    while prime <= math.ceil(math.sqrt(a)):
        if a % prime == 0:
            a /= prime
            count.append(prime)
            if len(count) == 2:
                if not a in count:
                    print("YES")
                    print(count[0], count[1], int(a))
                    break
        prime += 1
    else:
        print("NO")

