**Time limit:**1.00 s**Memory limit:**512 MB

At each step, a child can give one unit of food to his or her neighbour. What is the minimum number of steps needed?

**Input**

The first input line contains an integer $n$: the number of children.

The next line has $n$ integers $a_1,a_2,\ldots,a_n$: the current amount of food for each child.

The last line has $n$ integers $b_1,b_2,\ldots,b_n$: the required amount of food for each child.

**Output**

Print one integer: the minimum number of steps.

**Constraints**

- $1 \le n \le 2 \cdot 10^5$

- $0 \le a_i, b_i \le 10^6$

**Example**

Input:

`3`

3 5 0

2 4 2

Output:

`2`

Explanation: Child 1 gives one unit of food to child 3, and child 2 gives one unit of food to child 3.