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: Memory Limit Exceeded)

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

public class Main {

	public static void main(String[] args) throws IOException {
		// 10*10マス目の紙
		int paper[][] = new int[10][10];
		// 色がついてないマス目の個数
		int emptySpace = 0;
		// 1番濃いマス目の濃さ
		int max = 0;

		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String str = br.readLine();

		while (str != null) {
			// 文字列を指定した区切り文字(",")によって分割し,それぞれの配列の要素として格納する
			String[] array = str.split(",");
			int x = Integer.parseInt(array[0]);
			int y = Integer.parseInt(array[1]);
			int size = Integer.parseInt(array[2]);

			drop(paper, x, y, size);
		}

		// 色のついてない部分のマス目の個数と、1番濃いマス目の濃さを格納
		for (int i = 0; i < 10; i++) {
			for (int j = 0; j < 10; j++) {
				if (paper[i][j] == 0) {
					emptySpace++;
				}else if (paper[i][j] > max) {
					max = paper[i][j];
				}
			}
		}

		System.out.println(emptySpace);
		System.out.println(max);
	}

	// ぞれぞれのサイズに合わせた滴下メソッド呼び出す
	private static void drop(int paper[][], int x, int y, int size) {
		if (size == 1) {
			drop1(paper, x, y);
		}
		if (size == 2) {
			drop2(paper, x, y);
		}
		if (size == 3) {
			drop3(paper, x, y);
		}
	}

	// サイズ小の滴下メソッド
	private static void drop1(int paper[][], int x, int y) {
		paper[x][y]++;
		if (x + 1 < 10) {
			paper[x + 1][y]++;
		}
		if (x - 1 > -1) {
			paper[x - 1][y]++;
		}
		if (y + 1 < 10) {
			paper[x][y + 1]++;
		}
		if (y - 1 > -1) {
			paper[x][y - 1]++;
		}
	}

	// サイズ中の滴下メソッド
	private static void drop2(int paper[][], int x, int y) {
		drop1(paper, x, y);
		if (x + 1 < 10 && y + 1 < 10) {
			paper[x + 1][y + 1]++;
		}
		if (x + 1 < 10 && y - 1 > -1) {
			paper[x + 1][y - 1]++;
		}
		if (x - 1 > -1 && y + 1 < 10) {
			paper[x - 1][y + 1]++;
		}
		if (x - 1 > -1 && y - 1 > -1) {
			paper[x - 1][y - 1]++;
		}
	}

	// サイズ大の滴下メソッド
	private static void drop3(int paper[][], int x, int y) {
		drop2(paper, x, y);
		if (x + 2 < 10) {
			paper[x + 2][y]++;
		}
		if (x - 2 > -1) {
			paper[x - 2][y]++;
		}
		if (y + 2 < 10) {
			paper[x][y + 2]++;
		}
		if (y - 2 > -1) {
			paper[x][y - 2]++;
		}
	}
}