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
tests = int(input())

prime = [1 for i in range(10**6)]
prime[0] = 0
prime[1] = 0

for i in range(2,10**6):
    if(prime[i] == 1):
        for j in range(i*i,10**6,i):
            prime[j] = 0
        
#prime_list = []
for te in range(tests):
    n = int(input())
    count = 0
    prime_list = []
    for i in range(2,int(math.sqrt(n))+2):
        if(prime[i] == 1):
            while(n%i == 0):
                n = n//i
                prime_list.append(i)
                count += 1
    if(n>1):
        count += 1
        prime_list.append(n)
    pro = [0 for i in range(len(prime_list))]
    #print(len(prime_list))
    #print(prime_list)
    #print(len(pro))
    pro[0] = prime_list[0]
    flag = 0
    for i in range(1,len(prime_list)):
        pro[i] = pro[i-1]*prime_list[i]
    #print(pro)
    if(count > 2):
        for i in range(len(prime_list)-2):
            for j in range(i+1,len(prime_list)-1):
                a = pro[i]
                b = pro[j]//pro[i]
                c = pro[len(prime_list)-1]//pro[j]
                if(a!=b and b!=c and a!=c):
                    print('YES')
                    print(a,end = ' ')
                    print(b,end = ' ')
                    print(c,end = '\n')
                    flag = 1
                    break
            if(flag == 1):
                break
                    
        if(flag == 0):
            print('NO')
    else:
        print('NO')