It is 2:00 AM, and Ritisha is ready to leave the Duck Lounge and head home. Fortunately, the city is arranged as a grid, and a rideshare car is waiting for her.

The Duck Lounge is at the intersection ~(x_s,y_s)~, and Ritisha's home is at ~(x_h,y_h)~. During each minute, the car can move at most ~a~ blocks horizontally and at most ~b~ blocks vertically. These movements happen at the same time.

More precisely, in one minute the car may change its ~x~-coordinate by any integer between ~-a~ and ~a~, and its ~y~-coordinate by any integer between ~-b~ and ~b~. The car must remain at intersections with integer coordinates. There are no obstacles or one-way streets.

Find the minimum number of minutes Ritisha needs to reach home.

Input

The first line contains four integers ~x_s~, ~y_s~, ~x_h~, and ~y_h~ (~-10^9 \leq x_s,y_s,x_h,y_h \leq 10^9~): the coordinates of the Duck Lounge and Ritisha's home.

The second line contains two integers ~a~ and ~b~ (~1 \leq a,b \leq 10^9~): the maximum horizontal and vertical distances the car can travel in one minute.

Output

Output a single integer: the minimum number of minutes Ritisha needs to reach home.

Examples

Input 1

11 8 2 3
4 2

Output 1

3

The car must travel ~9~ blocks horizontally and ~5~ blocks vertically. It can travel ~4~ blocks horizontally per minute, and ~2~ vertically per minute. After ~3~ minutes, it can reach Ritisha's home.

Input 2

-5 12 8 -2
6 4

Output 2

4