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 cal1(n,tmp):
    i = 2
    while i*i<=n:
        if n % i == 0:
            if (i != n//i and i != tmp and n//i != tmp):
                return (tmp,i,n//i)
        i+=1
    return (-1,0,0)

def cal(n):
    i = 2
    while i*i<=n:
        if n % i == 0 and n//i != i:
            #i, n//i
            res ,a,b = cal1(n//i,i)
            if res != -1:
                return (1,res,a,b)

        i+=1
    return (0,0,0,0)

for i in range(int(input())):
    n = int(input())
    res,a,b,c = cal(n)
    if res == 1:
        print('YES')
        print(a,b,c)
    else:
        print('NO')