Problem Statement

Tiles are laid out on a coordinate plane. There are two types of tiles: small tiles of size $1\times1$ and large tiles of size $K\times K,$ laid out according to the following rules:

• For each pair of integers (i,j), the square $\lbrace(x,y)\mid i\leq x\leq i+1\wedge j\leq y\leq j+1\rbrace$ is contained within either one small tile or one large tile.
• If $\left\lfloor\dfrac iK\right\rfloor+\left\lfloor\dfrac jK\right\rfloor$ is even, it is contained within a small tile.
• Otherwise, it is contained within a large tile.

Tiles include their boundaries, and no two different tiles have a positive area of intersection.
For example, when K=3, 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 movement any number of times:

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

Each time he crosses from one tile to another, he must pay a toll of 1.
Determine the minimum toll Takahashi must pay to reach the point (T_x+0.5,T_y+0.5).

Input

The input is given from Standard Input in the following format:
K
S_x S_y
T_x T_y

Output

Print the minimum toll Takahashi must pay.

Constraints

• $1\leq K\leq10^{16}$
• $0\leq S_x\leq2\times10^{16}$
• $0\leq S_y\leq2\times10^{16}$
• $0\leq T_x\leq2\times10^{16}$
• $0\leq T_y\leq2\times10^{16}$
• All input values are integers.

Sample Input 1

3
7 2
1 6

Sample Output 1

5

For example, he can move as follows, paying a toll of 5.

• Move up by 3. Pay a toll of 1.
• Move left by 2. Pay a toll of 1.
• Move up by 1. Pay a toll of 1.
• Move left by 4. Pay a toll of 2.

The toll paid cannot be 4 or less, so print 5.

Sample Input 2

1
41 42
13 56

Sample Output 2

42

When he moves the shortest distance, he will always pay a toll of 42.
The toll paid cannot be 41 or less, so print 42.

Sample Input 3

100
100 99
199 1

Sample Output 3

0

There are cases where no toll needs to be paid.

Sample Input 4

96929423
5105216413055191 10822465733465225
1543712011036057 14412421458305526

Sample Output 4

79154049

见题面 Input 部分

见题面 Output 部分