Practice Geometry with the exercise "Inside Area"

Learning Opportunities

This puzzle can be solved using the following concepts. Practice using these concepts and improve your skills.

Geometry

Statement

Goal

A robot is navigating a 2D plane, following a set of movement instructions.
The following symbols are used to indicate the movement directions:
^ : Move up
v : Move down
> : Move right
< : Move left

Each instruction consists of a direction and an integer step indicating the number of units to move in that direction. For example, "> 5" means the robot will move 5 units to the right.

After executing all instructions, the robot returns to its starting point, creating a closed, non-self-intersecting polygon.

Example:
4
> 3
v 2
< 3
^ 2

The robot will make a path looks like:

......
.####.
.#..#.
.####.
......

We want to know the area enclosed by the robot's path, including the path.
It looks like:

......
.####.
.####.
.####.
......

So, the area is 12.

Can you determine the enclosed area based on the given set of instructions?

Input

line 1: number of instructions n
following n lines: one instruction in each row. formatted as direction step, meaning that the robot should move step units in direction

Output

line 1: area inside the path, including the path.

Constraints

Example

Input

4
< 6
^ 4
> 6
v 4

Output

Solve it

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