Problem Description

A snail is crawling across an infinite grid of equally sized squares. It can crawl horizontally (east and west) or vertically (north and south), but it cannot crawl diagonally.

As the snail crawls, it leaves a trail of slime which makes the squares of the grid it touches slimy.

For example, after the snail below crawls east 3 squares, there will be 4 slimy squares as shown.

Given the movements taken by the snail, your job is to determine how many times the snail enters a slimy square.

Input Specification

The first line of input contains a positive integer, M, representing the number of movements taken by the snail.

The next M lines will specify the snail’s movements, in order. Each movement will contain an uppercase directional letter (N, E, S, or W), followed by a positive integer less than or equal to 20 representing the number of squares the snail crawls in that direction.

The following table shows how the 15 available marks are distributed:

Marks	Description	Bound
4	The snail will never crawl north or west of its initial position and will stay close to its initial position.	M ≤ 20
3	The snail will stay close to its initial position.
6	The snail may crawl quite far from its initial position.	M ≤ 1200
2	The snail may crawl extremely far from its initial position.	M ≤ 200000

La version fran¸caise figure `a la suite de la version anglaise.

Output Specification

Output the non-negative integer, T, which is the number of times the snail enters a slimy square.

Sample Input 1

3

S2

N2

S3

Output for Sample Input 1

4

Explanation of Output for Sample Input 1

The diagram shows the snail’s path. Whenever the snail enters a slimy square, a numbered circle is placed along the path.

Notice that a single slimy square can be entered multiple times.

Sample Input 2

3

S2

W15

N20

Output for Sample Input 2

0

Explanation of Output for Sample Input 2

The snail’s path will consist of 38 slimy squares. However, the snail never returns to a square after leaving it, so the snail never enters a slimy square.

Technical Notes

You might receive an unpredictable error message if your program uses too much memory.

Python 3 submissions for this problem will be evaluated using the standard interpreter python3 (Version 3.10.12) instead of pypy3 7.3 . 9 (Version 3.8.13).