In the world of tiles, there is a famous tiles maker who takes order for making tiles. The specialty about him is that he always creates square tiles and likes to cover up the given area using minimum number of tiles.

Input

The input line contains two positive integers, m and n (0 ≤ m, n ≤ 10000), indicating the length and width of the area to cover with tiles. Your program should run until the end of file.

Output

For each input line, you have to find out the minimum number of square tiles to cover up the entire area.

Remember the tiles provider gets very happy when a prime number of tiles are used and gets unhappy otherwise. So, print a smiley ":)" in case of prime or ":(" for otherwise, after a space while printing the last line of a test case. In case, no tiles can be fitted in the area print “Area cannot be covered. :|”.

Sample

Input

Output

3 1
13 29
10 10
2 8

1 x 1 tiles required 3
In total minimum 3 tiles required. :)
13 x 13 tiles required 2
3 x 3 tiles required 4
1 x 1 tiles required 3
In total minimum 9 tiles required. :(
10 x 10 tiles required 1
In total minimum 1 tile required. :(
2 x 2 tiles required 4
In total minimum 4 tiles required. :(