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:
for _ in range(int(input())):
    n = int(input())
    a = []
    for i in range(2,int((n**0.5))+1):
        if n%i == 0:
            n=n//i
            a.append(i)
            break
    if len(a)==1 :
        for j in range(a[0]+1,int((n**0.5))+1):
            if n%j == 0:
                n=n//j
                a.append(j)
                break
    a.append(n)
    if len(a) == 3 and a[1]<a[2]:
        print("YES")
        print(*a)
    else:
        print("NO")