Nene and the Passing Game

篮球队有 $n$ 名队员，标号为 $1\sim n$，第 $i$ 名队员的手臂长度范围为 $[l_i,r_i]$，$i,j(i\ne j)$ 两名球员能互相传球当且仅当 $|i-j|\in [l_i+l_j,r_i+r_j]$。 现在要进行若干次训练，每次训练可用一个长为 $m$ 的序列 $p$ 描述。首先队员 $p_1$ 拿到球，然后传给 $p_2$，$p_2$ 传给 $p_3$，以此类推，直到 $p_{m-1}$ 传给 $p_m$。需要保证序列中相邻的两名队员可以互相传球，每名队员可以在序列中出现多次。 教练希望进行最少次数的训练，使得每位球员都在某次训练中出现。求训练次数的最小值。每个测试点 $t$ 组测试用例。 - $1\le t\le 2\cdot 10^5;$ - $1\le n\le 2\cdot 10^6;$ - $\sum n\le 2\cdot 10^6;$ - $1\le l\le r\le n$。 Translated by [Luzhuoyuan](https://www.luogu.com.cn/user/388940).

Nene is training her team as a basketball coach. Nene's team consists of $ n $ players, numbered from $ 1 $ to $ n $ . The $ i $ -th player has an arm interval $ [l_i,r_i] $ . Two players $ i $ and $ j $ ( $ i \neq j $ ) can pass the ball to each other if and only if $ |i-j|\in[l_i+l_j,r_i+r_j] $ (here, $ |x| $ denotes the absolute value of $ x $ ). Nene wants to test the cooperation ability of these players. In order to do this, she will hold several rounds of assessment. - In each round, Nene will select a sequence of players $ p_1,p_2,\ldots,p_m $ such that players $ p_i $ and $ p_{i+1} $ can pass the ball to each other for all $ 1 \le i < m $ . The length of the sequence $ m $ can be chosen by Nene. Each player can appear in the sequence $ p_1,p_2,\ldots,p_m $ multiple times or not appear in it at all. - Then, Nene will throw a ball to player $ p_1 $ , player $ p_1 $ will pass the ball to player $ p_2 $ and so on... Player $ p_m $ will throw a ball away from the basketball court so it can no longer be used. As a coach, Nene wants each of $ n $ players to appear in at least one round of assessment. Since Nene has to go on a date after school, Nene wants you to calculate the minimum number of rounds of assessment needed to complete the task.

Each test contains multiple test cases. The first line contains the number of test cases $ t $ ( $ 1 \le t \le 2\cdot 10^5 $ ). The description of test cases follows. The first line contains a single integer $ n $ ( $ 1 \le n \le 2\cdot 10^6 $ ) — the number of players. The $ i $ -th of the next $ n $ lines contains two integers $ l_i $ and $ r_i $ ( $ 1\leq l_i\leq r_i\leq n $ ) — the arm interval of the $ i $ -th player. It is guaranteed that the sum of $ n $ over all test cases does not exceed $ 2\cdot 10^6 $ .

For each test case, output one integer — the minimum number of rounds of assessment Nene needs to complete her work.

5
2
1 1
1 1
2
1 1
2 2
3
1 3
1 3
1 3
5
1 1
2 2
1 5
2 2
1 1
6
1 2
5 5
2 3
2 3
2 2
1 2

2
2
2
1
3

In the first two test cases, Nene can host two rounds of assessment: one with $ p=[1] $ and one with $ p=[2] $ . It can be shown that hosting one round of assessment is not enough, so the answer is $ 2 $ . In the third test case, Nene can host two rounds of assessment: one with $ p=[1,3] $ and one with $ p=[2] $ . Player $ 1 $ can pass the ball to player $ 3 $ as $ |3-1|=2 \in [1+1,3+3] $ . It can be shown that hosting one round of assessment is not enough, so the answer is $ 2 $ .