B. Knishop
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

I would've won this game if my knight can move diagonally like a bishop!

Yifan created an imaginary piece, knishop, in order to win in a chess tournament. It can move like a knight or a bishop in all moves. More formally, if a knishop is currently at coordinate $$$(x,y)$$$:

  1. As a knight, it can move to $$$(x+2,y+1),(x+2,y-1),(x-2,y+1),(x-2,y-1),(x+1,y+2),(x+1,y-2),(x-1,y+2),(x-1,y-2)$$$.
  2. As a bishop, it can move to $$$(x+a,y+a),(x+a,y-a)$$$ for any integer $$$a$$$.

In Yifan's imagination, a chessboard is a cartesian plane without a boundary. In other words, pieces can move to any point with integer coordinates, like $$$(-1,-2)$$$. To test the power of this piece, Yifan wants to move his knishop from $$$(x_1,y_1)$$$ to $$$(x_2,y_2)$$$ in the minimum number of moves. Find the minimum number of moves needed.

Input

The first line contains 4 integers $$$x_1,y_1,x_2,y_2$$$ $$$(-10^9\le x_1,y_1,x_2,y_2\le 10^9)$$$.

Output

The minimum number of moves needed.

Examples
Input
0 0 1 2
Output
1
Input
1 1 -100 -100
Output
1
Note

In the first example, the knishop moves like a knight.

In the second example, the knishop moves diagonally, like a bishop.