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 t in range (t):
    n=int(input())
    d=2
    cate=0
    vec=[0]*10
    while d*d <= n:
        if(n%d == 0 and cate<2):
            vec[cate]=d
            cate+=1
            n/=d
        if cate == 2:
            break
        d+=1
    if n > 1 and cate == 2:
        vec[cate]=n
        cate+=1
    if cate < 3 or vec[2] == vec[1]:
        print("NO")
    else:
        print("YES")
        print(int(vec[0]),int(vec[1]),int(vec[2]))