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 

n = int(input())

def sd(n, notin):
    i = 2
    while i * i < n:
        if n % i == 0 and i not in notin:
            return i
        i += 1
    
    return n

for i in range(n):
    a = int(input())
    aa = a
    sq = int(math.sqrt(a)) + 1

    divisor = []
    while True:
        s = sd(a, divisor)
        if s == a:
            print("NO")
            break
        a = a // s

        divisor.append(s)
        if len(divisor) == 2:

            if a != divisor[0] and a != divisor[1]:
                print("YES")
                print(divisor[0], divisor[1], a)
            else:
                print("NO")
            break
    