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())

while t:
    n=int(input())
    
    cnt=0
    i=2
    ans=[]
    while True:
        while i*i<n:
            if n%i==0:
                ans.append(i)
                cnt+=1
                if cnt==2:
                    ans.append(int(n/i))
                    break
                n=n/i
            i+=1
        if i*i>=n or cnt==2:
            break
    
    if cnt==2:
        print("YES")
        print(*ans,sep=' ')
    else:
        print("NO")
    
    t-=1