Problem Description

Farmer John’s $N$ cows are very picky about the temperature inside their barn. Some cows like it cooler, while others like it warmer.

Farmer John’s barn contains a row of $N$ stalls, numbered $1 \ldots N$, with one cow in each stall. The $i$-th cow wants the temperature in her stall to be $p_i$, but the current temperature in her stall is $t_i$. To make sure every cow feels comfortable, Farmer John installed a new air-conditioning system. The way this system is controlled is quite special: he can send a command to the system telling it to increase or decrease the temperature of a continuous group of stalls by 1 unit—for example, “increase the temperature of stalls $5 \ldots 8$ by 1 unit.” A continuous group of stalls can be as short as a single stall.

Please help Farmer John find the minimum number of commands he must send to the new air-conditioning system so that every stall’s temperature matches the ideal temperature of the cow in that stall.

Input Format

The first line contains $N$. The next line contains $N$ non-negative integers $p_1 \ldots p_N$, separated by spaces. The last line contains $N$ non-negative integers $t_1 \ldots t_N$.

Output Format

Output one integer: the minimum number of commands Farmer John needs to use.

5
1 5 3 3 4
1 2 2 2 1

5

Hint

【Sample Explanation】

One optimal set of commands Farmer John can use is:

Initial temperatures        : 1 2 2 2 1
Increase stalls 2..5 by 1   : 1 3 3 3 2
Increase stalls 2..5 by 1   : 1 4 4 4 3
Increase stalls 2..5 by 1   : 1 5 5 5 4
Decrease stalls 3..4 by 1   : 1 5 4 4 4
Decrease stalls 3..4 by 1   : 1 5 3 3 4

【Constraints】

• Test cases 2-5 satisfy $N \leq 100$.
• Test cases 6-8 satisfy $N \leq 1000$.
• Test cases 9-10 satisfy $N \leq 100,000$.
• In test cases 1-6 and 9, temperature values do not exceed $100$.
• In test cases 7-8 and 10, temperature values do not exceed $10,000$.

Translated by ChatGPT 5