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:
t = int(input())

def fd(n):
    a = []
    
    for i in range(2, 1+int(n**0.5)):
        if n%i == 0:
            a.append(i)
            a.append(n//i)
            
    return list(set(a))

for _ in range(t):
    n = int(input())
    found = False
    
    d = fd(n)
    
    for i in d:
        tt = fd(n//i)
        if len(tt) > 1 and tt[0] != tt[-1] and tt[0] != i and tt[-1] != i and tt[0]*tt[-1]*i == n:
            print("YES")
            print(tt[0],tt[-1],i)
            found = True
            break
    
    if not found:
        print("NO")