Task Processing

Yeongseon works today, and she works tomorrow and the day after as well.

Yeongseon has been assigned $n$ tasks. Each task can be done only inside a fixed period, and the time it takes depends on the day she starts it.

Suppose a task has period $[a, b]$. If she starts it on day $d$ and it takes $T$ days, she works from day $d$ through day $d + T - 1$ and finishes on day $d + T - 1$. So she can start that task on day $d$ only when $a \le d$ and $d + T - 1 \le b$.

For example, take a task with period $[1, 5]$ that takes 4 days when started on day 1, 2 days on day 2, 3 days on day 3, 5 days on day 4, and 2 days on day 5. Starting on day 4 or on day 5 runs past day 5, so the task cannot finish inside its period. Starting on day 2 finishes it on day 3, which is the earliest possible.

Yeongseon handles one task at a time. If the previous task finished on day $e$, the next task may start on that same day $e$.

She does not have to do every task. Given the task information, find the largest number of tasks she can finish.

The first line contains the number of tasks $n$. ($1 \le n \le 15$)

Each of the next $n$ lines describes one task. The line starts with two integers $a$ and $b$, followed by $b - a + 1$ integers. Those integers are the times $T_i$ the task takes when it is started on day $a$, day $a + 1$, $\dots$, day $b$, in that order. ($1 \le a \le b \le 100$, $1 \le T_i \le 100$)

Print the largest number of tasks that can be finished.