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:
m=int(input())
for l in range(m):
    n=int(input())
    q,t=int(n**.5)+1,0
    for i in range(2,q):
        if n%i==0:
            a=n//i
            w=int(a**.5)+1
            for j in range(2,w):
                if a%j==0:
                    r=a//j
                    if r!=j and j!=i and r!=i:
                        print("YES")
                        print(i,j,r)
                        t=1
                        break
        if t:
            break
    if not t:
        print("NO")