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 _ in [0]*int(input()):
    n = int(input())
    i = 2
    tt = False
    delim = []
    while i*i <= n:
        if not n % i:
            delim.append(i)
        i += 1
    for i in range(len(delim)):
        if tt == True:
            break
        for j in range(i+1, len(delim)):
            f = n // (delim[i]*delim[j])
            if f > 1 and f not in (delim[i], delim[j]) and not n % (delim[i]*delim[j]):
                tt = True
                print("YES")
                print(delim[i], delim[j], f)
                break
    if tt == False:
        print("NO")