Avoid Rainbow Cycles

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

There are two arrays of positive integers a_1, a_2, …, a_m and b_1, b_2, …, 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 ∈ 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 → e_1 → i_2 → e_2 → … → i_k → e_k → 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 ≤ m, n ≤ 10^5), the number of sets and the number of vertices in the graph.

The second line contains m integers a_1, a_2, …, a_m (1 ≤ a_i ≤ 10^9).

The third line contains n integers b_1, b_2, …, b_n (1 ≤ b_i ≤ 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 ≤ s_i ≤ 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 ≤ i ≤ m does not exceed 2 ⋅ 10^5.

Output

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

Examples

Input

3 2 1 2 3 4 5 2 1 2 2 1 2 2 1 2

Output

11

Input

7 8 3 6 7 9 10 7 239 8 1 9 7 10 2 6 239 3 2 1 3 2 4 1 3 1 3 7 2 4 3 5 3 4 5 6 7 2 5 7 1 8

Output

66

Note

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.

inputFormat

Input

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

The second line contains m integers a_1, a_2, …, a_m (1 ≤ a_i ≤ 10^9).

The third line contains n integers b_1, b_2, …, b_n (1 ≤ b_i ≤ 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 ≤ s_i ≤ 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 ≤ i ≤ m does not exceed 2 ⋅ 10^5.

outputFormat

Output

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

Examples

Input

3 2 1 2 3 4 5 2 1 2 2 1 2 2 1 2

Output

11

Input

7 8 3 6 7 9 10 7 239 8 1 9 7 10 2 6 239 3 2 1 3 2 4 1 3 1 3 7 2 4 3 5 3 4 5 6 7 2 5 7 1 8

Output

66

Note

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.

样例

7 8
3 6 7 9 10 7 239
8 1 9 7 10 2 6 239
3 2 1 3
2 4 1
3 1 3 7
2 4 3
5 3 4 5 6 7
2 5 7
1 8

66

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