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: Accepted)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class Main {

	// インク滴を落とすマス
	private int[][] cell = new int[10][10];

	public static void main(String[] args) throws Exception {
		new Main().execute();
	}

	/**
	 * 計算実行
	 */
	private void execute() throws IOException {

		// 標準入力
		BufferedReader reader = new BufferedReader(new InputStreamReader(
				System.in));

		// 標準入力を１行ずつ処理
		String line = null;
		while ((line = reader.readLine()) != null) {
			String[] inkInfo = line.split(",");

			// インクを落とした結果を紙に反映
			calcInkDropPoint(Integer.parseInt(inkInfo[0]),
					Integer.parseInt(inkInfo[1]), Integer.parseInt(inkInfo[2]));
		}

		// 結果を出力
		outputInkDropPoint();

	}

	/**
	 * インク滴を落とした結果を紙に反映
	 * 
	 * @param x
	 *            X座標
	 * @param y
	 *            Y座標
	 * @param size
	 *            インク滴のサイズ
	 */
	private void calcInkDropPoint(int x, int y, int size) {

		// インクが落ちた箇所にポイント加算
		cell[x][y] += 1;

		// 小の滴が落ちた座標にポイント加算
		addPoint(x + 1, y);
		addPoint(x - 1, y);
		addPoint(x, y + 1);
		addPoint(x, y - 1);

		// 中の滴が落ちた座標にポイント加算
		if (size > 1) {
			addPoint(x + 1, y + 1);
			addPoint(x - 1, y + 1);
			addPoint(x + 1, y - 1);
			addPoint(x - 1, y - 1);
		}

		// 大の滴が落ちた座標にポイント加算
		if (size > 2) {
			addPoint(x + 2, y);
			addPoint(x - 2, y);
			addPoint(x, y + 2);
			addPoint(x, y - 2);
		}

	}

	/**
	 * インク滴を落とした結果を出力 「色のついていない部分のマス目の個数」と「１番濃いマス目の濃さ」を出力する。
	 */
	private void outputInkDropPoint() {

		int totalCell = 0;
		int maxPoint = 0;

		for (int i = 0; i < cell.length; i++) {
			for (int j = 0; j < cell[i].length; j++) {

				// 色のついていないセル個数を計算
				if (cell[i][j] == 0) {
					totalCell += 1;
				}

				// 最高得点の計算
				if (cell[i][j] > maxPoint) {
					maxPoint = cell[i][j];
				}
			}
		}

		// 結果を標準出力
		System.out.println(totalCell);
		System.out.println(maxPoint);
	}

	/**
	 * インク滴が滲む範囲か判定
	 * 
	 * @param direction
	 *            座標
	 * @return 判定結果(true:範囲内、false:範囲外)
	 */
	private boolean isInsideOfCell(int direction) {
		return (direction >= 0) && (direction < 10);
	}

	/**
	 * インク滴が滲む範囲であれば加算
	 * 
	 * @param x
	 *            X座標
	 * @param y
	 *            Y座標
	 */
	private void addPoint(int x, int y) {
		// 範囲内であれば加点
		if (isInsideOfCell(x) && isInsideOfCell(y)) {
			cell[x][y] += 1;
		}
	}

}