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:
for _ in range(int(input())):
    n=int(input())
    a=0
    b=0
    c=0
    for i in range(2,int(n**0.5)+1):
        if n%i==0:
            a=i
            t=n//i
            for j in range(a+1,int(t**0.5)+1):
                if t%j==0:
                    b=j
                    c=t//j
                    if b==c:
                        b=0
                        c=0
                        continue
                    break
            break
    if a and b and c:
        print('YES')
        print(a,b,c)
    else: print('NO')