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 prime(n):
    if n == 1:
        return []
    if n == 2:
        return [2]
    i = 2
    while i*i <= n:
        if n%i == 0:
            return prime(n//i)+[i]
        i += 1
    return [n]
    
for _ in range(int(input())):
    n = int(input())
    a = sorted(prime(n))
    if len(set(a)) >= 3:
        print("YES")
        prod = 1
        for x in a[1:-1]:
            prod *= x
        print(a[0], prod, a[-1])
    if len(set(a)) == 2:
        if len(a) >= 4:
            print("YES")
            prod = 1
            for x in a[1:-1]:
                prod *= x
            print(a[0], prod, a[-1])
        else:
            print("NO")
    if len(set(a)) == 1:
        if len(a) >= 6:
            print("YES")
            print(a[0], a[0]*a[0], a[0]**(len(a)-3))
        else:
            print("NO")
    if a == []:
        print("NO")