import java.util.Collections;
import java.util.HashSet;
import java.util.List;
import java.util.Set;

final class Matrix {

  private final List<List<Integer>> values;

  Matrix(final List<List<Integer>> values) {
    this.values = values;
  }

  Set<MatrixCoordinate> getSaddlePoints() {
    final Set<MatrixCoordinate> result = new HashSet<>();

    if (values.isEmpty()) {
      return result;
    }

    for (int row = 0; row < values.size(); row++) {
      for (int column = 0; column < values.get(0).size(); column++) {
        final int coordinateValue = values.get(row).get(column);

        if (coordinateValue == getRowMax(row) && coordinateValue == getColumnMin(column)) {
          result.add(new MatrixCoordinate(row, column));
        }
      }
    }

    return result;
  }

  private int getRowMax(final int row) {
    return Collections.max(values.get(row));
  }

  private int getColumnMin(final int column) {
    return values.stream()
        .map(row -> row.get(column))
        .min(Integer::compareTo)
        .orElseThrow(() -> new IllegalArgumentException("Column cannot be empty"));
  }

}