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 range(int(input())):
    n = int(input())
    ok = False
    for i in range(2, int(n**0.5)+1):
        if n % i ==0:
            p = n//i
            if p == i:
                continue
            for j in range(i+1, int(p**0.5)+1):
                if p%j == 0:
                    if j*j!=p and p//j != i:
                        print('YES')
                        print(i,j,p//j)
                        ok = True
                        break
        if ok:
            break
    if not ok:
        print('NO')