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:
def affichage(L):
          for i in range(len(L)):
                    L[i]=str(L[i])
          return(' '.join(L))
t=int(input())

for i in range(t):
    n=int(input())
    n1=n
    nb=0
    x=int(n**0.5)
    X=[]
    for i in range(2,x+1):
        if n%i==0:
            n=n//i
            X.append(i)
            nb+=1
            if nb==2:
                break

    if nb==2:
        X.append(n1//(X[-1]*X[-2]))
        if X[0]!=X[1] and X[1]!=X[2] and X[0]!=X[2]:
            print("YES")
            print(affichage(X))
        else:
            print("NO")
    else:
        print("NO")