Travel

Yan enjoys travelling around the country of Iatiland in his car.

Since Yan has been travelling for a long time, he has come up with a description of the map of the whole country. The cities in Iatiland are numbered from $1$ to $N$, and there are bi-directional direct roads connecting pairs of different cities. For each city, he has a list of cities that are reachable from it using a direct road. It is guaranteed that there is a unique path between every pair of cities. Note that the path may not be direct, i.e. it may use several direct roads. This means that there are a total of $N - 1$ direct roads.

Yan likes travelling systematically, so he follows an algorithm while going around the country.

He starts his journey in city $1$ on day $1$. Every subsequent day he follows a direct road from the city he is currently in. The road he chooses is always the first road in the list of the current city. After picking the road, he removes it from the beginning of the list and appends it to the end.

Yan's main objective is to meet his friends and gossip with them. He has $M$ friends, numbered from $1$ to $M$, and friend $i$ lives in city $P_i$. He can visit friend $i$ only when he is currently in city $P_i$. Yan wants to visit his friends in the given order, so he cannot visit friend $i + 1$ before visiting friend $i$.

Find the minimal number of days before he visits all of his friends in the correct order.

The first line contains two numbers $N$ and $M$.

This is followed by $N$ lines. On line $i$, there is $k_i$, the number of direct paths coming out of city $i$, followed by $k_i$ numbers, the initial list of cities to which city $i$ is connected by a direct path.

The last line contains $M$ numbers $P_i$, the cities where Yan's friends live.

Output the minimum number of days on a single line.

• $1 \le N \le 5 \times 10^5$
• $1 \le M \le 5 \times 10^5$
• $1 \le k_i \le N - 1$
• $1 \le P_i \le N$