Tommy has a binary tree rooted at ~1~ on ~n~ nodes. Each node has an integer weight ~w_i~, and the father of node ~i = 2, 3, \dots, n~ is ~f_i~. Tommy needs to disassemble this binary tree by sequentially removing edges. When an edge ~(u, v)~ is removed, the following happen, simultaneously:

• ~w_u+w_v~ units of cost are incurred;
• ~w_u~ and ~w_v~ are swapped.

Find the minimum units of cost necessary to disassemble the binary tree.

Constraints

~2 \le n \le 5000~

~1 \le w_i \le 10^9~

Test	~n \le~
1 - 3	~10~
4 - 7	~100~
8 - 11	~500~
12 - 16	~1\,000~
17 - 25	~5\,000~

Input Specification

The first line contains a positive integer ~n~.

The second line contains ~n~ positive integers ~w_1, w_2, \dots, w_n~.

The third line contains ~n-1~ positive integers ~f_2, f_3, \dots, f_n~, describing the binary tree.

Output Specification

Output the answer.

Sample Input 1

3
2 1 3
1 1

Sample Output 1

7

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