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:
def min_dev(n,temp):
    while temp<n**0.5+1:
        if n%temp==0:
            return temp
        temp+=1
    return 0
for _ in range(int(input())):
    n=int(input())
    a=min_dev(n,2)
    if a==0:
        print('NO')
        continue
    b=min_dev(int(n/a),a+1)
    if b==0:
        print('NO')
        continue
    c=int(n/(a*b))
    if c==0 or c==b or c==1 or c==a:
        print('NO')
        continue
    print('YES')
    print(a,b,c)