Alex on his walk to Forest of leaf discovers $N$ sticks lying in front of him. Each stick has two values represented by two arrays $arr$ and $price$ of size $N$ where in array $arr$, $arr[i]$ $(0 <= i <= N-1)$ denotes length of $i'th$ stick and array $price$, $price[i]$ $(0 <= i <= N-1)$ denotes price to increment length of $i'th$ stick by $1$ unit.

Alex calls an array Broken Adjacency when none of the adjacent sticks has equal length. A stick $i$ is adjacent to stick $i-1$ (if any) and stick $i+1$ (if any). He wants to find the minimum cost to achieve Broken Adjacency. To do so, in 1 move he can increment the length of any $i'th$ stick by $1$ unit at the price of $price[i]$.

Can you help him find the minimum cost to achieve his goal?

Input Format:

• The first line contains an integer $T$ denoting the number of test cases.
• The first input line of each test case contains one integer $N$, denoting the number of sticks found.
• The second line contains $N$ space-separated integers denoting the elements of array $arr$.
• The third line contains $N$ space-separated integers denoting the elements of array $price$.

Output Format:

Print the minimum cost to make given sticks to Broken Adjacent sticks.

Constraints:

$1 <= T <= 10$

$1 <= N <= 10^5$

$1 <= arr[i] <= 10^9$

$1 <= price[i] <= 10^9$