Submissions are evaluated using the multi-class logarithmic loss. Each `id` in the test set had a single true class label, `Status`. For each `id`, you must submit a set of predicted probabilities for each of the three possible outcomes, e.g., `Status_C`, `Status_CL`, and `Status_D`.

The metric is calculated

$$log loss = -\frac{1}{N}\sum_{i=1}^N\sum_{j=1}^My_{ij}\log(p_{ij}),$$

where \\(N\\) is the number of rows in the test set, \\(M\\) is the number of outcomes (i.e., 3),  \\(log\\) is the natural logarithm, \\(y_{ij}\\) is 1 if row \\(i\\) has the ground truth label \\(j\\) and 0 otherwise, and \\(p_{ij}\\) is the predicted probability that observation \\(i\\) belongs to class \\(j\\).

The submitted probabilities for a given row are not required to sum to one because they are rescaled prior to being scored (each row is divided by the row sum). In order to avoid the extremes of the log function, predicted probabilities are replaced with \\(max(min(p,1-10^{-15}),10^{-15})\\).

## Submission File
For each `id` row in the test set, you must predict probabilities of the three outcomes `Status_C`, `Status_CL`, and `Status_D` . The file should contain a header and have the following format:

    id,Status_C,Status_CL,Status_D
    7905,0.628084,0.034788,0.337128
    7906,0.628084,0.034788,0.337128
    7907,0.628084,0.034788,0.337128
    etc.