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:
import math
def prime(n):
    flag=0
    for i in range(2,int(math.sqrt(n))+1):
        if(n%i==0):
            flag=1
            break
    if(flag!=1):
        return 1
    else:
        return 0
t=int(input())
while(t!=0):
    n=int(input())
    n1=n
    flag=0
    if((prime(n)==0) and n>=24):
        for i in range(2,int(math.sqrt(n))+1):
            if(n%i==0):
                a=i
                break
        if(prime(n//a)==0):
            n=n//a
            for i in range(2,int(math.sqrt(n))+1):
                if((n%i==0) and i!=a and (n//i)!=a and (n//i)!=i):
                    b=i
                    c=n//b
                    flag=1
                    break
    if(flag!=0 and a>=2 and b>=2 and c>=2 and (a*b*c)==n1):
        print("YES")
        print(a,b,c)
    else:
        print("NO")
    t-=1