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 t in range(int(input())):
    n=int(input())
    flag=0
    for i in range(2,10001):
        if(n%i==0):
            flag=1
            break
    if(flag==1):
        a=i
        n=n//i
        for i in range(2,100001):
            if(n%i==0 and i!=a):
                flag=2
                break
    b=i
    c=n//i
    if(flag==2 and b!=c and c!=1 and c!=a):
        print("YES")
        print(a,b,c)
    else:
        print("NO")