Practice Conditions and Trigonometry with the exercise "Static Equilibrium"

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Statement

Goal

This problem aims to find a single force that can put a point mass in motion to a static equilibrium in a two-dimensional space.

A point mass is in static equilibrium if the resultant forces in both the x and y directions are zero.

You are given a list of forces, each described by a magnitude and a direction. Each force acts along one of the four cardinal directions:

- RIGHT → positive x-direction (0°)
- LEFT → negative x-direction (180°)
- UP → positive y-direction (90°)
- DOWN → negative y-direction (270°)

Your task is to find the magnitude of the force that will balance all the given forces, as well as its angle measured anti-clockwise from the positive x-axis (RIGHT).

Here is a step-by-step guide:

1. Sum all forces in the x-direction (forces labelled LEFT and RIGHT). Assign negative values to forces acting in the negative x-direction (LEFT). Call this sum Fx.

2. Sum all forces in the y-direction (forces labelled UP and DOWN). Assign negative values to forces acting in the negative y-direction (DOWN). Call this sum Fy.

3. To find the components of the balancing force that will bring the point mass into equilibrium, multiply Fx and Fy by -1. These new values are your balancing force components, i.e. x = -Fx and y = -Fy .

4. Calculate the magnitude of this balancing force using the formula, corrected to the nearest hundredth. For example: 5.3659 ==> 5.37.
result = square root of ( x squared + y squared )

5. Determine the angle theta, measured anti-clockwise from the positive x-axis (RIGHT).

If both x and y are zero, return 0.00 for both result and theta.

Example (refer to test case 1)
1. We will proceed by summing all the forces according to their directions:
Fx = 45 - 20 = 25
Fy = 30 - 40 = -10

2. Calculate x and y:
x = -Fx = -25
y = -Fy = +10

3. Calculate the magnitude of the balancing force:
Balancing Force = sqrt[(-25)^2+10^2] = 26.93

4. Calculate the angle of the force:
As x is negative and y is positive, theta = 180° - arctan(10 / |-25|) = 158.20

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Input

Line 1: An integer n, for the number of forces.
Next n lines: Magnitude of the force F (integer), and the direction the force is acting dir (string), separated by a space.

Output

Line 1: The balancing force, result, corrected to two decimal places.
Line 2: The angle of the balancing force theta in degrees, measured anti-clockwise from the positive x-axis (RIGHT), corrected to two decimal places.

Constraints

1 ≤ n ≤ 1000
1 ≤ F ≤ 1000000
0° ≤ theta ≤ 360°
The direction dir of the input can only be UP, DOWN, LEFT or RIGHT.

Example

Input

4
30 UP
45 RIGHT
40 DOWN
20 LEFT

Output

26.93
158.20

Solve it

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