You are given $m$ sets of integers $A_1, A_2, \ldots, A_m$; elements of these sets are integers between $1$ and $n$, inclusive.

There are two arrays of positive integers $a_1, a_2, \ldots, a_m$ and $b_1, b_2, \ldots, b_n$.

In one operation you can delete an element $j$ from the set $A_i$ and pay $a_i + b_j$ coins for that.

You can make several (maybe none) operations (some sets can become empty).

After that, you will make an edge-colored undirected graph consisting of $n$ vertices. For each set $A_i$ you will add an edge $(x, y)$ with color $i$ for all $x, y \in A_i$ and $x < y$. Some pairs of vertices can be connected with more than one edge, but such edges have different colors.

You call a cycle $i_1 \to e_1 \to i_2 \to e_2 \to \ldots \to i_k \to e_k \to i_1$ ($e_j$ is some edge connecting vertices $i_j$ and $i_{j+1}$ in this graph) rainbow if all edges on it have different colors.

Find the minimum number of coins you should pay to get a graph without rainbow cycles.

Input

The first line contains two integers $m$ and $n$ ($1 \leq m, n \leq 10^5$), the number of sets and the number of vertices in the graph.

The second line contains $m$ integers $a_1, a_2, \ldots, a_m$ ($1 \leq a_i \leq 10^9$).

The third line contains $n$ integers $b_1, b_2, \ldots, b_n$ ($1 \leq b_i \leq 10^9$).

In the each of the next of $m$ lines there are descriptions of sets. In the $i$-th line the first integer $s_i$ ($1 \leq s_i \leq n$) is equal to the size of $A_i$. Then $s_i$ integers follow: the elements of the set $A_i$. These integers are from $1$ to $n$ and distinct.

It is guaranteed that the sum of $s_i$ for all $1 \leq i \leq m$ does not exceed $2 \cdot 10^5$.

Output

Print one integer: the minimum number of coins you should pay for operations to avoid rainbow cycles in the obtained graph.

见题面 Input 部分

见题面 Output 部分

In the first test, you can make such operations:

• Delete element $1$ from set $1$. You should pay $a_1 + b_1 = 5$ coins for that.
• Delete element $1$ from set $2$. You should pay $a_2 + b_1 = 6$ coins for that.

You pay $11$ coins in total. After these operations, the first and the second sets will be equal to $\{2\}$ and the third set will be equal to $\{1, 2\}$.

So, the graph will consist of one edge $(1, 2)$ of color $3$.

In the second test, you can make such operations:

• Delete element $1$ from set $1$. You should pay $a_1 + b_1 = 11$ coins for that.
• Delete element $4$ from set $2$. You should pay $a_2 + b_4 = 13$ coins for that.
• Delete element $7$ from set $3$. You should pay $a_3 + b_7 = 13$ coins for that.
• Delete element $4$ from set $4$. You should pay $a_4 + b_4 = 16$ coins for that.
• Delete element $7$ from set $6$. You should pay $a_6 + b_7 = 13$ coins for that.

You pay $66$ coins in total.

After these operations, the sets will be:

• $\{2, 3\}$;
• $\{1\}$;
• $\{1, 3\}$;
• $\{3\}$;
• $\{3, 4, 5, 6, 7\}$;
• $\{5\}$;
• $\{8\}$.

We will get the graph:

There are no rainbow cycles in it.