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 petit(a,k):
    for i in range(a+1,int(k**0.5)+1):
        if k%i==0:
            return i, k//i
    return -1, -1

n = int(input())
for i in range(n):
    k = int(input())
    a1, k2 = petit(1, k)
    if a1==-1:
        print('NO')
    else:
        a2, a3 = petit(a1,k2)
        if a2==-1:
            print('NO')
        elif (a2 == a3) or (a3 == a1):
            print('NO')
        else:
            print('YES')
            print(a1, a2, a3)