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 solution():
    temp = [True]*31623
    for i in range(2, 31623):
        if temp[i]:
            for j in range(i+i, 31623, i):
                temp[j] = False
    er = [i for i, v in enumerate(temp) if v][2:]
    for _ in range(int(input())):
        n = int(input())
        ans = set()
        er_iter = er.__iter__()
        current = er_iter.__next__()
        l = 1
        while current < n:
            if n%current == 0:
                if current in ans:
                    if l == 1:
                        l = current
                    else:
                        ans.add(current*l)
                        l = 1
                else:
                    ans.add(current)
                n //= current
                if len(ans) == 2 and n not in ans: break
            else:
                try:
                    current = er_iter.__next__()
                except StopIteration:
                    break
        if l:
            n *= l
        if len(ans) == 2 and n not in ans:
            print("YES")
            ans.add(n)
            print(*ans)
        else:
            print("NO")
solution()