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 s(a,b):
    i = b+1
    c = int(a**0.5)
    while 1:
        if a%i==0:
            return i
        else:
            if i<c:
                i+=1
            else:
                return 1

for _ in range(int(input())):
    n = int(input())
    a = s(n,1)
    #print(a)
    if a==1 or a==n:
        print('NO')
    else:
        a1 = n//a
        a2 = s(a1,a)
        if a2==1 or a2==a1:
            print('NO')
        else:
            a3 = a1//a2
            b = sorted([a,a2,a3])
            if len(set(b))==3:
                print('YES')
                print(b[0],b[1],b[2])
            else:
                print('NO')