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:
# cook your dish here
import math

def primeFactors(n): 
    arr=[]
    while n % 2 == 0: 
        arr.append(2)
        n = n / 2
        
    for i in range(3,int(math.sqrt(n))+1,2): 

        while n % i== 0: 
            arr.append(i)
            n = n / i 

    if n > 2: 
        arr.append(n)
    return arr

t=int(input())
for _ in range(t):
    n=int(input())
    arr=primeFactors(n)
    if len(arr)>=3:
        a=arr[0]
        if arr[0]!=arr[1]:
            b=arr[1]
            c=n//(a*b)
            if c==a or c==b or c<2:
                print("NO")
            else:
                print("YES")
                print(a,b,c)
        else:
            b=arr[1]*arr[2]
            c=n//(a*b)
            if c==a or c==b or c<2:
                print("NO")
            else:
                print("YES")
                print(a,b,c)
    else:
        print("NO")