There has been an earthquake in the advanced city of Chongmetry, which is built entirely from mathematical formulas. All the bridges have been destroyed, and you have been hired to repair them.

You have been given x and y-coordinates from the still standing parts of the bridges. You are also given the x positions of the broken parts of the bridges, where new pillars are supposed to be built. Your job is to determine the height of these pillars, so the bridge forms its original shape.

For this task we have given you training data and it’s not allowed to find your own training data on the internet.

Input

Download the file with training and test data. These can be found at the bottom under “attachments”. You will receive a zip file containing:

• train.csv - data describing the whole parts of the bridges with x and y positions.

• test.csv - data describing positions where pillars are supposed to be built for each bridge.

The train.csv file contains:

• x - East-West Position in meters.

• y - North-South Position in meters.

• function_id - The unique id for a particular bridge.

The test.csv file contains:

• x - The East-West Position in meters

• function_id - The unique id for a particular bridge.

Output

For each row in test.csv, output the predicted y-coordinate for the height of the bridge at that position.

Example

Input (test.csv)

x, bridge_id
0.0230414009098678,0
0.2002533893994107,0
0.2434611332892733,0
0.2465272413496277,0

Output

-0.8987764984440185
-0.8976034961618553
-0.8970351768669409
-0.8969906419752334

Scoring

If $D$ is the average of all differences between your predicted y-coordinate and the true y-coordinate capped at 0.5. In other words, $D = \frac{1}{n} \sum _{i=1}^{n} \min (0.5, |y_i - y_i'|)$.

The final score is calculated by comparing your solution’s average error, $D$, to two reference values: an ideal score, $B_\text {best} = 0.1$, and a baseline score, $B_\text {baseline} = 0.5$. Lower error results in a higher score.

Specifically, the formula is:

At the end of the competition, all solutions will be retested on the remaining 70% of the data. Your final score at the end of the competition will only be based on the remaining 70% of the data; the 30% tested during the competition will have no effect. It is guaranteed that the 30% tested during the competition were chosen uniformly at random and are entirely disjoint from the 70% tested at the end. Therefore, the results on the 30% tested during the competition should be seen as a strong indicator of how well your solution performs. At the same time, it is detrimental to overfit your solution to the test data.