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:
n=int(input())
for i in range (n):
    a=int(input())
    A=[]  
    for i in range (2, int(a**(0.5))):
        if a%i==0:
            A.append(i)
            a/=i
            break
    if (len(A) == 0):
        print("NO")
        continue
    else:
        for i in range (A[0] + 1, int(a**0.5)+1):
            if a %i==0:
                A.append(i)
                a/=i
                break
        if len(A)==2:
            if A[1]==a or A[0]==1:
                print("NO")
            else:
                print("YES")
                print(A[0], A[1], int(a))     
        else:
            print("NO")