Given ~N~ horizontal lines and ~M~ vertical lines, count the number of squares in the grid. For example, a horizontal line could be ~y = 3~ or ~y = 1~, etc. Furthermore, vertical lines could be ~x = 2~ or ~x = 5~. The lines of the cartesian grid will never start at a negative position in both the y-axis and x-axis.

The whole boundary of the square has to be drawn. The inside of the square does not have to be empty.

Input Specification

The first line of input will contain 2 integers, ~N~ and ~M~ ~(0 \le N, M \le 1200)~.

The next line of input will contain ~N~ integers ~a_i~, indicating that the line ~y = a_i~ exists.

The next line of input will contain ~M~ integers ~b_i~, indicating that the line ~x = b_i~ exists.

~0 \le a_i, b_i \le 10^5~

Output Specification

Output the total number of squares.

Sample Input

3 4
0 1 3
1 2 4 8

Sample Output

3

There is one ~1 \times 1~ square, one ~2 \times 2~ square, and one ~3 \times 3~ square.