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:
num = int(input())
mas = [None] * num
for i in range(num):
    mas[i] = int(input())
    

for i in range(num):
    n = mas[i]
    n0 = n
    i = 2
    delit = []
    while i * i <= n0:
        while n % i == 0:
            delit.append(i)
            n //= i
        i += 1
    if n != 1:
        delit.append(n)
        
  
    if len(set(delit)) == 1 and len(delit) > 5:
        print("YES")
        print(delit[0], delit[0] * delit[0], n0 // delit[0] ** 3)
    elif (len(set(delit)) == 2 and len(delit) > 3) or len(set(delit)) > 2:
        print("YES")
        a = delit[0]
        b = delit[-1]
        print(a, b, n0 // (a * b))
    else:
        print("NO")