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 is_prime(n):
    isPrime=1
    for i in range(2,math.floor(math.sqrt(n))+1):
        if n%i==0:
            isPrime=1
            break
    if isPrime==1:
        return False
    return True
    
for _ in range(int(input())):
    n=int(input())
    isPrime = is_prime(n)
    if isPrime:
        print("NO")
    else:
        a,b,c = 0,0,0
        l=[]
        k=n
        for i in range(2,math.floor(math.sqrt(n))+1):
            if n%i==0:
                if (n//i==i):
                    l.append(i)
                else:
                    l.append(i)
                    l.append(n//i)
        l.append(k)
        a=min(l)
        
        if (a!=0):
            l=[]
            n=k//a
            for i in range(2,math.floor(math.sqrt(n))+1):
                if n%i==0:
                    if (n//i==i):
                        if i>a:
                            l.append(i)
                    else:
                        if i>a:
                            l.append(i)
                        if n//i>a:
                            l.append(n//i)
            l.append(k//a)
            b=min(l)
            
        if (b!=0):
            l=[]
            n=k//(a*b)            
            for i in range(2,math.floor(math.sqrt(n)+1)):
                if n%i==0:
                    if (n//i==i):
                        if i>b:
                            l.append(i)
                    else:
                        if i>b:
                            l.append(i)
                        if n//i>b:
                            l.append(n//i)
            l.append(k//(a*b))
            
            c=max(l)
         
 
        if (len(set([a,b,c]))<3) or a<2 or b<2 or c<2:
            print("NO")
        else:
            print("YES")
            print(a,b,c)