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())

def factor(n):
    arr = set({})
    for i in range(2, int(n**0.5)+1):
        if n % i == 0:
            arr.add(i)
            arr.add(int(n/i))
    return arr

def find(n, arr):
    for a in arr:
        for b in arr:
            for c in arr:
                if (a != b) and (b != c) and (a != c) and a*b*c == n:
                    print('YES')
                    return str(a) + ' ' + str(b) + ' ' + str(c)
    return 'NO'

for _ in range(t):
    n = int(input())
    arr = factor(n)
    print(find(n, arr))