Meeting

A board with $N$ members is planning to have a meeting. Due to the large number of board members, it is difficult to find a time that suits everyone, but the aim is to have as many people as possible attend the meeting.

Each member is available during a number of different time intervals, where each time interval $[a, b]$ means that the member can attend if the meeting starts at some time $t$ where $a \le t \le b$. Since some members are very careless with their calendars, the same member may accidentally give you overlapping time intervals, e.g., $[1, 3]$ and $[2, 4]$, even though one interval would have sufficed, in this case $[1, 4]$.

Calculate the maximum number of members who can attend the meeting.

Input

The first line contains an integer $N$ ($1 \le N \leq 2\cdot 10^5$), the number of members on the board.

This is followed by $N$ lines, one for each board member. The $i$-th line starts with the number of time intervals $m_ i$ ($1 \leq m_ i \leq 2\cdot 10^5$) during which the $i$-th member can attend. This is followed by $m_ i$ pairs of integers, one for each interval. These pairs $a, b$ ($0 \le a \le b \le 10^9$) represent the interval $[a, b]$.

Let $B=\sum _{i=1}^{N} m_ i$ be the sum of the number of time intervals during which all members are available. It is given that $B \leq 2\cdot 10^5$.

Output

Print a single line with an integer – the maximum number of members that can attend the meeting if the start time is chosen optimally.

Scoring

Your solution will be tested on a set of test groups, each worth a number of points. Each test group contains a set of test cases. To get the points for a test group you need to solve all test cases in the test group.

Explanation of Samples

In the first example, we can choose to start the meeting at time $4$, when members $2$ and $3$ can attend. This case could be included in all test case groups.

Examples $2$ and $3$ could not be included in test case groups $2$ or $3$.

3
2 1 3 5 6
4 1 10 11 12 17 18 14 15
1 4 4

2

3
3 2 8 2 7 5 6
4 7 15 15 20 9 13 18 20
3 12 19 9 16 12 16

2

3
2 5 14 0 20
3 5 16 5 11 8 9
2 7 11 7 18

3