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())
 
for i in range(t):
    count = 0
    flag = 0
    a = []
    n = int(input())
    for j in range(2,int(n**0.5)+1):
        if (count == 2 and n < j):
            print("NO")
            flag = 1
            break
        elif (count == 2 and n>j):
            print("YES")
            for x in a:
                print(x,end = " ")
            print(int(n))
            count = count + 1
            break
        elif(count == 2 and n == j):
            if j in a:
                print("NO")
                flag = 1
                break
            else:
                print("YES")
                for x in a:
                    print(x,end = " ")
                print(int(n))
                count = count + 1
                break
        if( n % j == 0):
            if j not in a:
                n = n/j
                count += 1
                a.append(j)
    if (count <=2 and flag == 0):
        print("NO")