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 _ in range(t):
    n = int(input())
    ans = [-1,-1,-1]
    i = 2
    now = 0
    while i**2 <= n:
        if n%i == 0:
            ans[now] = i
            n//=i
            if now == 1:break
            now += 1
        i += 1
    if n >= 2:
        ans[2] = n
    if ans[1] != -1 and ans[2] == n and ans[1] != ans[2]:
        print("YES")
        print(*ans)
    else:
        print("NO")