Score : $350$ points

问题陈述

坐标平面上覆盖着 $2\times1$ 的瓷砖。这些瓷砖按照以下规则铺设：

• 对于整数对 $(i,j)$，正方形 $A _ {i,j}=\lbrace(x,y)\mid i\leq x\leq i+1 \wedge j\leq y\leq j+1\rbrace$ 包含在一个瓷砖内。
• 当 $i+j$ 为偶数时，$A _ {i,j}$ 和 $A _ {i + 1,j}$ 包含在同一个瓷砖内。

瓷砖包括它们的边界，并且没有两个不同的瓷砖共享一个正面积。

在原点附近，瓷砖的铺设方式如下：

高桥从坐标平面上的点 $(S _ x+0.5,S _ y+0.5)$ 开始。

他可以重复以下移动任意次数：

• 选择一个方向（上、下、左或右）和一个正整数 $n$。在那个方向上移动 $n$ 个单位。

每次他进入一个瓷砖，他需要支付 1 元的通行费。

找出他到达点 $(T _ x+0.5,T _ y+0.5)$ 必须支付的最小通行费。

以上为大语言模型 kimi 翻译，仅供参考。

Problem Statement

The coordinate plane is covered with $2\times1$ tiles. The tiles are laid out according to the following rules:

• For an integer pair $(i,j)$, the square $A _ {i,j}=\lbrace(x,y)\mid i\leq x\leq i+1\wedge j\leq y\leq j+1\rbrace$ is contained in one tile.
• When $i+j$ is even, $A _ {i,j}$ and $A _ {i + 1,j}$ are contained in the same tile.

Tiles include their boundaries, and no two different tiles share a positive area.

Near the origin, the tiles are laid out as follows:

Takahashi starts at the point $(S _ x+0.5,S _ y+0.5)$ on the coordinate plane.

He can repeat the following move as many times as he likes:

• Choose a direction (up, down, left, or right) and a positive integer $n$. Move $n$ units in that direction.

Each time he enters a tile, he pays a toll of $1$.

Find the minimum toll he must pay to reach the point $(T _ x+0.5,T _ y+0.5)$.

Constraints

• $0\leq S _ x\leq2\times10 ^ {16}$
• $0\leq S _ y\leq2\times10 ^ {16}$
• $0\leq T _ x\leq2\times10 ^ {16}$
• $0\leq T _ y\leq2\times10 ^ {16}$
• All input values are integers.

Input

The input is given from Standard Input in the following format:

$S _ x$ $S _ y$

$T _ x$ $T _ y$

Output

Print the minimum toll Takahashi must pay.

Sample Input 1

5 0
2 5

Sample Output 1

5

For example, Takahashi can pay a toll of $5$ by moving as follows:

• Move left by $1$. Pay a toll of $0$.
• Move up by $1$. Pay a toll of $1$.
• Move left by $1$. Pay a toll of $0$.
• Move up by $3$. Pay a toll of $3$.
• Move left by $1$. Pay a toll of $0$.
• Move up by $1$. Pay a toll of $1$.

It is impossible to reduce the toll to $4$ or less, so print 5.

Sample Input 2

3 1
4 1

Sample Output 2

0

There are cases where no toll needs to be paid.

Sample Input 3

2552608206527595 5411232866732612
771856005518028 7206210729152763

Sample Output 3

1794977862420151

Note that the value to be output may exceed the range of a $32$-bit integer.