Busy Robot

题意翻译

### 题意翻译 你有一个机器人，初始位置（ $0$ 秒），它在数轴上的位置为 $0$ 。 它会接收 $n$ 个命令：在第 $t_i$ 秒移动到 $x_i$ 。在它移动的时候，会忽视你的所有命令。 定义第 $i$ 个命令是成功的，当且仅当在第 $[t_i,t_{i+1}]$ 秒内机器人到达过 $x_i$ 。（我们定义 $t_{n+1}$ 为正无穷） 你的任务就是求出有多少条命令是成功的。 ### 输入格式 第 $1$ 行， $1$ 个数 $t$ ，表示数据组数。 >每组数据的第 $1$ 行为 $n$ 。 > >接下来 $n$ 行，每行两个数 $t_i$ ， $x_i$ 。 ### 输出格式 $t$ 行，每行一个数，表示这组数据中成功的命令数量。 ### 数据规模与约定 $1 \leq t \leq 1000$ $1 \leq n \leq 10^5$ $1 \leq t_i \leq 10^9$ $-10^9 \leq x_i \leq 10^9$ 每组数据中 $n$ 的和不超过 $10^5$ 数据保证 $t_i$ 单调递增

题目描述

You have a robot that can move along a number line. At time moment $ 0 $ it stands at point $ 0 $ . You give $ n $ commands to the robot: at time $ t_i $ seconds you command the robot to go to point $ x_i $ . Whenever the robot receives a command, it starts moving towards the point $ x_i $ with the speed of $ 1 $ unit per second, and he stops when he reaches that point. However, while the robot is moving, it ignores all the other commands that you give him. For example, suppose you give three commands to the robot: at time $ 1 $ move to point $ 5 $ , at time $ 3 $ move to point $ 0 $ and at time $ 6 $ move to point $ 4 $ . Then the robot stands at $ 0 $ until time $ 1 $ , then starts moving towards $ 5 $ , ignores the second command, reaches $ 5 $ at time $ 6 $ and immediately starts moving to $ 4 $ to execute the third command. At time $ 7 $ it reaches $ 4 $ and stops there. You call the command $ i $ successful, if there is a time moment in the range $ [t_i, t_{i + 1}] $ (i. e. after you give this command and before you give another one, both bounds inclusive; we consider $ t_{n + 1} = +\infty $ ) when the robot is at point $ x_i $ . Count the number of successful commands. Note that it is possible that an ignored command is successful.

输入输出格式

输入格式

The first line contains a single integer $ t $ ( $ 1 \le t \le 1000 $ ) — the number of test cases. The next lines describe the test cases. The first line of a test case contains a single integer $ n $ ( $ 1 \le n \le 10^5 $ ) — the number of commands. The next $ n $ lines describe the commands. The $ i $ -th of these lines contains two integers $ t_i $ and $ x_i $ ( $ 1 \le t_i \le 10^9 $ , $ -10^9 \le x_i \le 10^9 $ ) — the time and the point of the $ i $ -th command. The commands are ordered by time, that is, $ t_i < t_{i + 1} $ for all possible $ i $ . The sum of $ n $ over test cases does not exceed $ 10^5 $ .

输出格式

For each testcase output a single integer — the number of successful commands.

输入输出样例

输入样例 #1

8
3
1 5
3 0
6 4
3
1 5
2 4
10 -5
5
2 -5
3 1
4 1
5 1
6 1
4
3 3
5 -3
9 2
12 0
8
1 1
2 -6
7 2
8 3
12 -9
14 2
18 -1
23 9
5
1 -4
4 -7
6 -1
7 -3
8 -7
2
1 2
2 -2
6
3 10
5 5
8 0
12 -4
14 -7
19 -5

输出样例 #1

1
2
0
2
1
1
0
2

说明

The movements of the robot in the first test case are described in the problem statement. Only the last command is successful. In the second test case the second command is successful: the robot passes through target point $ 4 $ at time $ 5 $ . Also, the last command is eventually successful. In the third test case no command is successful, and the robot stops at $ -5 $ at time moment $ 7 $ . Here are the $ 0 $ -indexed sequences of the positions of the robot in each second for each testcase of the example. After the cut all the positions are equal to the last one: 1. $ [0, 0, 1, 2, 3, 4, 5, 4, 4, \dots] $ 2. $ [0, 0, 1, 2, 3, 4, 5, 5, 5, 5, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -5, \dots] $ 3. $ [0, 0, 0, -1, -2, -3, -4, -5, -5, \dots] $ 4. $ [0, 0, 0, 0, 1, 2, 3, 3, 3, 3, 2, 2, 2, 1, 0, 0, \dots] $ 5. $ [0, 0, 1, 0, -1, -2, -3, -4, -5, -6, -6, -6, -6, -7, -8, -9, -9, -9, -9, -8, -7, -6, -5, -4, -3, -2, -1, -1, \dots] $ 6. $ [0, 0, -1, -2, -3, -4, -4, -3, -2, -1, -1, \dots] $ 7. $ [0, 0, 1, 2, 2, \dots] $ 8. $ [0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, -7, -7, \dots] $