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:

n = int(input())


for k in range(n):
    z = int(input())
    l = []
    for i in range(2 , z):
        if z % i == 0:
            l.append(i)
            z = z // i
            break
        if (i * i) > z:
            break
    for j in range(2 , z):
        if z % j == 0 and j not in l:
            l.append(j)
            z = z // j
            break
        if (j * j) > z:
            break
    if len(l) < 2 or z == 1 or z in l:
        print('NO')
    else:
        print('YES')
        print(l[0] , l[1] , z)