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 _ in range(t):

    n = int(input())
    i = 2
    arr = [0,0,0]
    k = 0
    while(i * i <= n):
        if (n % i == 0):
            arr[k] = i
            n = int(n/i)
            k+=1
        if (k == 2):
            break
        i+=1
    arr[2] = n
    if(arr[1] >1 and arr[0] > 1 and arr[2] > 1):
        if (arr[0] == arr[1] or arr[1] == arr[2] or arr[0] == arr[1]):
            print ("NO")
        else:
            print("YES")
            print(str(arr[0]) + " " + str(arr[1]) + " " + str(arr[2]))
    else:
        print("NO")