Problem:
Score : 200 points

Problem Statement

In a factory, there are N robots placed on a number line.
Robot i is placed at coordinate X_i and can extend its arms of length L_i in both directions, positive and negative.

We want to remove zero or more robots so that the movable ranges of arms of no two remaining robots intersect.
Here, for each i (1 \leq i \leq N), the movable range of arms of Robot i is the part of the number line between the coordinates X_i - L_i and X_i + L_i, excluding the endpoints.

Find the maximum number of robots that we can keep.

Constraints

1 \leq N \leq 100,000

0 \leq X_i \leq 10^9 (1 \leq i \leq N)

1 \leq L_i \leq 10^9 (1 \leq i \leq N)

If i \neq j, X_i \neq X_j.

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
X_1 L_1
X_2 L_2
\vdots
X_N L_N

Output

Print the maximum number of robots that we can keep.

Sample Input 1

4
2 4
4 3
9 3
100 5

Sample Output 1

3

By removing Robot 2, we can keep the other three robots.

Sample Input 2

2
8 20
1 10

Sample Output 2

1

Sample Input 3

5
10 1
2 1
4 1
6 1
8 1

Sample Output 3

5

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)


import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.Comparator;
import java.util.StringTokenizer;

/**
 * for (int i = 0; i < N; i++) {}
 * System.out.println();
 * HashMap<Integer, Integer> hm = new HashMap<>();
 * int[] s = new int[M];
 * ArrayDeque<Integer> deq = new ArrayDeque<>();
 *
 */
public class Main implements Runnable { //クラス名はMain1

	public static void main(String[] args) {
		Thread.setDefaultUncaughtExceptionHandler((t, e) -> System.exit(1));
		new Thread(null, new Main(), "", 1024 * 1024 * 1024).start(); //16MBスタックを確保して実行
	}

	public void run() {
		FastScannerMain1 sc = new FastScannerMain1(System.in);

		try {
			//String S = sc.nextLine().trim();
			int N = sc.nextInt();
			Robot[] r = new Robot[N];

			//long l = sc.nextLong();
			//ArrayList<Integer> arr = new ArrayList<Integer>();

			for (int i = 0; i < N; i++) {
				int start = sc.nextInt();
				int length = sc.nextInt();
				int end = start + length;
				Robot robot = new Robot();
				robot.start = start;
				robot.length = length;
				robot.end = end;
				r[i] = robot;
			}

			Arrays.sort(r, new Comparator<Robot>() {
				public int compare(Robot robot1, Robot robot2) {
					return robot1.end - robot2.end;
				}
			});

			int end = -1;
			int ans = 0;
			for (int i = 0; i < N; i++) {
				//System.out.println(r[i].start + " " + r[i].length + " " + r[i].end);
				if (r[i].start > end && end < r[i].end) {
					end = r[i].end;
					ans++;
				}

			}

			System.out.println(ans);

		} catch (Exception e) {
			e.printStackTrace();
		}

	}
}

class Robot {
	int start;
	int length;
	int end;
}

//高速なScanner
class FastScannerMain1 {
	private BufferedReader reader = null;
	private StringTokenizer tokenizer = null;

	public FastScannerMain1(InputStream in) {
		reader = new BufferedReader(new InputStreamReader(in));
		tokenizer = null;
	}

	public String next() {
		if (tokenizer == null || !tokenizer.hasMoreTokens()) {
			try {
				tokenizer = new StringTokenizer(reader.readLine());
			} catch (IOException e) {
				throw new RuntimeException(e);
			}
		}
		return tokenizer.nextToken();
	}

	public String nextLine() {
		if (tokenizer == null || !tokenizer.hasMoreTokens()) {
			try {
				return reader.readLine();
			} catch (IOException e) {
				throw new RuntimeException(e);
			}
		}
		return tokenizer.nextToken("\n");
	}

	public long nextLong() {
		return Long.parseLong(next());
	}

	public int nextInt() {
		return Integer.parseInt(next());
	}

	public double nextDouble() {
		return Double.parseDouble(next());
	}

	public int[] nextIntArray(int n) {
		int[] a = new int[n];
		for (int i = 0; i < n; i++)
			a[i] = nextInt();
		return a;
	}

	public long[] nextLongArray(int n) {
		long[] a = new long[n];
		for (int i = 0; i < n; i++)
			a[i] = nextLong();
		return a;
	}
}