CF1811B.Conveyor Belts

Conveyor matrix $m_n$ is matrix of size $n \times n$, where $n$ is an even number. The matrix consists of concentric ribbons moving clockwise.

In other words, the conveyor matrix for $n = 2$ is simply a matrix $2 \times 2$, whose cells form a cycle of length $4$ clockwise. For any natural $k \ge 2$, the matrix $m_{2k}$ is obtained by adding to the matrix $m_{2k - 2}$ an outer layer forming a clockwise cycle.

The conveyor matrix $8 \times 8$.

You are standing in a cell with coordinates $x_1, y_1$ and you want to get into a cell with coordinates $x_2, y_2$. A cell has coordinates $x, y$ if it is located at the intersection of the $x$th row and the $y$th column.

Standing on some cell, every second you will move to the cell next in the direction of movement of the tape on which you are. You can also move to a neighboring cell by spending one unit of energy. Movements happen instantly and you can make an unlimited number of them at any time.

Your task is to find the minimum amount of energy that will have to be spent to get from the cell with coordinates $x_1, y_1$ to the cell with coordinates $x_2, y_2$.

For example, $n=8$ initially you are in a cell with coordinates $1,3$ and you want to get into a cell with coordinates $6, 4$. You can immediately make $2$ movements, once you are in a cell with coordinates $3, 3$, and then after $8$ seconds you will be in the right cell.

传送带矩阵 $m_n$ 是一个大小为 $n \times n$ 的矩阵，其中 $n$ 为偶数。该矩阵由若干同心环形带组成，各环均顺时针移动。

换言之，当 $n = 2$ 时，传送带矩阵即为一个 $2 \times 2$ 矩阵，其所有单元格构成一个长度为 $4$ 的顺时针循环。对任意自然数 $k \ge 2$，矩阵 $m_{2k}$ 可通过在矩阵 $m_{2k - 2}$ 外围添加一层新的顺时针循环而得到。

$8 \times 8$ 传送带矩阵。

你起始于坐标为 $(x_1, y_1)$ 的单元格，并希望到达坐标为 $(x_2, y_2)$ 的单元格。某单元格的坐标为 $(x, y)$，表示它位于第 $x$ 行与第 $y$ 列的交点处。

当你站在某个单元格上时，每秒钟你将自动移向当前所在传送带运动方向上的下一个单元格。此外，你也可通过消耗 1 单位能量，瞬时移动至一个相邻单元格（上下左右四个方向之一）。此类能量驱动的移动可随时进行任意多次，且不耗时间。

你的任务是求出从坐标 $(x_1, y_1)$ 移动到坐标 $(x_2, y_2)$ 所需消耗的最少能量。

例如，当 $n = 8$ 时，你初始位于坐标 $(1,3)$ 的单元格，并希望到达坐标 $(6,4)$ 的单元格。你可以立即执行 2 次能量驱动的移动，使自己先到达坐标 $(3,3)$ 的单元格；随后经过 8 秒钟的自动传送，你将恰好抵达目标单元格。

The first line contains an integer $t$ ($1 \le t \le 2 \cdot 10^5$) — the number of test cases.

The descriptions of the test cases follow.

The description of each test case consists of one string containing five integers $n$, $x_1$, $y_1$, $x_2$ and $y_2$ ($1 \le x_1, y_1, x_2, y_2 \le n \le 10^9$) — matrix size and the coordinates of the start and end cells. It is guaranteed that the number $n$ is even.

第一行包含一个整数 $t$（$1 \le t \le 2 \cdot 10^5$）—— 测试用例的数量。

随后是各测试用例的描述。

每个测试用例的描述由一个字符串组成，其中包含五个整数 $n$、$x_1$、$y_1$、$x_2$ 和 $y_2$（$1 \le x_1, y_1, x_2, y_2 \le n \le 10^9$）—— 分别表示矩阵的大小以及起点和终点单元格的坐标。保证 $n$ 为偶数。

For each test case, print one integer in a separate line — the minimum amount of energy that will have to be spent to get from the cell with coordinates $x_1, y_1$ to the cell with coordinates $x_2, y_2$.

对于每个测试用例，在单独一行中输出一个整数——从坐标为 $x_1, y_1$ 的格子移动到坐标为 $x_2, y_2$ 的格子所需消耗的最少能量。