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:
t=int(input())
def printDivisors(n,a) :
    i=2
    f=0
    while(i*i<=n):
        if n%i==0:
            j=i+1
            n=n//i
            while(j*j<=n):
                if n%j==0:
                    if j!=n//j:
                        print('YES')
                        print(i,j,n//j)
                        f=1
                        break
                j+=1
            if f==1:
                break
        i+=1
    if f==0:
        print('NO')
                    
for _  in range(t):
    a=[]
    n=int(input())
    printDivisors(n,a)