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
m=1000000007
def fact(n):
    ans=1
    for i in range(1,n+1):
        ans=((ans%m)*(i%m))%m
    return ans

def power_2(n):
    ans=1
    for i in range(n):
        ans=((ans%m)*(2))%m
    return ans
    
for z in range(int(input())):
    n=int(input())
    fin=int(math.ceil(n**(1/3)))
    cnt,i=0,2

    # to find the first no in three we check the
    #value when it is less than cube root of n
    # becouse left no(2nd and 3rd) must be greater
    #than first becoz any no.less than first is not
    #able to divide n 
    while(i<=fin):
        if(n%i==0):
            cnt+=1
            n=int(n/i)
            break
        i+=1
        
    fin=int(math.ceil(n**(1/2)))
    j=i+1
    while(j<=fin):
        if(n%j==0 and j!=int(n/j) and int(n/j)!=i):
            cnt+=1
            break
        j+=1
        
    if(cnt==2):
        print("YES")
        print(i,j,int(n/j))
    else:
        print("NO")