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:
from math import sqrt
def two_dist(n, k):
    ans = []
    for i in range(2, int(sqrt(n))+5):
        if n % i == 0:
            if i != n//i and i != k and n//i != k and n//i >= 2:
                return [i, n//i]
    return False

for _ in range(int(input())):
    n = int(input())
    ans = []
    for p in range(2, int(sqrt(n))+4):
        if n % p == 0:
            find = two_dist(n//p, p)
            if find:
                ans = [p]+find
                break
    if ans:
        print("YES")
        print(" ".join(str(k) for k in ans))
    else:
        print("NO")