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())
for m in range(t):
    n= int(input())
    flag= 0
    u= int(pow(n,1/3))
    i=2
    while i<u+1:
        if(n%i==0):
            v= n/i
            f= int(pow(v,1/2))
            j= i+1
            while j<f+1:
                if(v%j==0):
                    v=v/j
                    flag=1
                    break
                j+=1
        if(flag==1):
            break
        i+=1
    if(flag==1 and j!=v):
        print('YES')
        print("%d   %d    %d" %(i,j,v))
    else:
        print('NO')