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 primeFactors(n):
    temp = []
    while n % 2 == 0: 
        temp.append(2)
        n = n / 2
    for i in range(3, int(math.sqrt(n))+1,2): 
        while n % i== 0: 
            temp.append(i)
            n = n / i 
    if n > 2: 
        temp.append(int(n))
    return temp
    
t = int(input())
while t:
    t += -1
    n = int(input())
    prime = primeFactors(n)
    if len(prime) < 3: print("NO")
    else:
        prime.sort()
        ans = [prime[0]]
        if prime[0] == prime[1]:
            ans.append(prime[1] * prime[2])
            p = 1
            for i in range(3, len(prime)):
                p *= prime[i]
            if p != 1: ans.append(p)
            if len(set(ans)) != 3: print("NO")
            else:
                print("YES")
                print(*ans)
        else:
            ans.append(prime[1])
            p = 1
            for i in range(2, len(prime)):
                p *= prime[i]
            if p != 1: ans.append(p)
            if len(set(ans)) != 3: print("NO")
            else:
                print("YES")
                print(*ans)