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 
def pro(j):
    for a in range(2,int(j**(1/3))+1):
        if j%a==0:
           for b in range(a+1,int(j**(1/2))): 
               if (j//a)%b==0 and (j//a)//b!=a and ((j//a)//b)!=int((j//a)**(1/2)):
                   print("YES")
                   print(a,b,(j//a)//b)
                   return
    print("NO")
    return
t=int(input())
l=[]
for i in range(t):
    n=int(input())
    l.append(n)
for j in l:
    pro(j)