Problem:
Dropping Ink

As shown in the following figure, there is a paper consisting of a grid structure where each cell is indicated by (x, y) coordinate system.

We are going to put drops of ink on the paper. A drop comes in three different sizes: Large, Medium, and Small. From the point of fall, the ink sinks into surrounding cells as shown in the figure depending on its size. In the figure, a star denotes the point of fall and a circle denotes the surrounding cells.

Originally, the paper is white that means for each cell the value of density is 0. The value of density is increased by 1 when the ink sinks into the corresponding cells.

For example, if we put a drop of Small ink at (1, 2) and a drop of Medium ink at (3, 2), the ink will sink as shown in the following figure (left side):

In the figure, density values of empty cells are 0. The ink sinking into out of the paper should be ignored as shown in the figure (top side). We can put several drops of ink at the same point.

Your task is to write a program which reads a sequence of points of fall (x, y) with its size (Small = 1, Medium = 2, Large = 3), and prints the number of cells whose density value is 0. The program must also print the maximum value of density.

You may assume that the paper always consists of 10 × 10, and 0 ≤ x < 10, 0 ≤ y < 10.

Input

x1,y1,s1
x2,y2,s2
:
:

(xi, yi) represents the position of the i-th drop and si denotes its size. The number of drops is less than or equal to 50.

Output

Print the number of cells whose density value is 0 in first line.

Print the maximum value of density in the second line.

Sample Input

2,5,3
3,6,1
3,4,2
4,5,2
3,6,3
2,4,1

Output for the Sample Input

77
5

Solution in JAVA (judge verdict: Wrong Answer)

import java.util.HashMap;
import java.util.Map;
import java.util.Scanner;

public class Main {
    /** フィールドサイズ[セル]：X */
    private static final int FIELD_SIZE_X = 10;

    /** フィールドサイズ[セル]：Y */
    private static final int FIELD_SIZE_Y = 10;

    /** 落とすインクとその後のフィールドの状態を保持するMap*/
    private static final Map<Integer, AbstractDropMode> droppedInkMap;

    static {
        // Mapの初期化
        droppedInkMap = new HashMap<Integer, Main.AbstractDropMode>();
        droppedInkMap.put(1, new StarMode(1));
        droppedInkMap.put(2, new SquareMode(1));
        droppedInkMap.put(3, new StarMode(2));
    }

    public static void main(String[] args) {
        try {
            // 場の初期化
            int[][] inkField = new int[FIELD_SIZE_X - 1][FIELD_SIZE_Y - 1];

            // input ループのためにScanner
            Scanner sc = new Scanner(System.in);

            // 入力に応じてインクを落とす
            while (sc.hasNext()) {
                String[] input = sc.next().split(",");
                int x = Integer.valueOf(input[0]);
                int y = Integer.valueOf(input[1]);
                int size = Integer.valueOf(input[2]);

                droppedInkMap.get(size).drop(inkField, x, y);
            }

            // 結果の主計
            System.out.println(countWhiteCells(inkField));
            System.out.println(getMostDroppedCount(inkField));

        } catch (Exception e) {
            e.printStackTrace();
            System.exit(0);
        }

    }

    private static int countWhiteCells(int[][] inkField) {
        int result = 0;
        for (int[] xField : inkField) {
            for (int cell : xField) {
                result = cell == 0 ? result + 1 : result;
            }
        }
        return result;
    }

    private static int getMostDroppedCount(int[][] inkField) {
        int result = 0;
        for (int[] xField : inkField) {
            for (int cell : xField) {
                result = cell > result ? cell : result;
            }
        }
        return result;
    }

    private abstract static class AbstractDropMode {
        protected int size;

        AbstractDropMode(int size) {
            this.size = size;
        }

        public abstract void drop(int[][] inkField, int dropPointX,
                int dropPointY);

        protected boolean isOverField(int point, int diff, int lowerLimit,
                int upperLimit) {
            return((point + diff) < lowerLimit || (point + diff) >= upperLimit);
        }
    }

    /** 四角形にインクを落とす<br> x = ±size, y = ±sizeの範囲にインクが落ちる */
    private static class SquareMode extends AbstractDropMode {
        SquareMode(int size) {
            super(size);
        }

        @Override
        public void drop(int[][] inkField, int dropPointX, int dropPointY) {
            for (int x = -1 * this.size; x <= this.size; x++) {
                // フィールド外なら処理しない
                if (isOverField(dropPointX, x, 0, inkField.length)) {
                    continue;
                }

                for (int y = -1 * this.size; y <= this.size; y++) {
                    if (isOverField(dropPointY, y, 0,
                            inkField[dropPointX + x].length)) {
                        continue;
                    }

                    inkField[dropPointX + x][dropPointY + y]++;
                }
            }
        }
    }

    /** 星形にインクを落とす<br> x + y = ±sizeの範囲にインクが落ちる */
    private static class StarMode extends AbstractDropMode {
        StarMode(int size) {
            super(size);
        }

        @Override
        public void drop(int[][] inkField, int dropPointX, int dropPointY) {
            for (int x = -1 * this.size; x <= this.size; x++) {
                // フィールド外なら処理しない
                if (isOverField(dropPointX, x, 0, inkField.length)) {
                    continue;
                }

                for (int y = -1 * (this.size - Math.abs(x)); y <= (this.size - Math
                        .abs(x)); y++) {

                    if (isOverField(dropPointY, y, 0,
                            inkField[dropPointX + x].length)) {
                        continue;
                    }

                    inkField[dropPointX + x][dropPointY + y]++;
                }
            }
        }
    }

}