Problem:
Score : 600 points

Problem Statement

There are N robots numbered 1 to N placed on a number line. Robot i is placed at coordinate X_i. When activated, it will travel the distance of D_i in the positive direction, and then it will be removed from the number line. All the robots move at the same speed, and their sizes are ignorable.

Takahashi, who is a mischievous boy, can do the following operation any number of times (possibly zero) as long as there is a robot remaining on the number line.

Choose a robot and activate it. This operation cannot be done when there is a robot moving.

While Robot i is moving, if it touches another robot j that is remaining in the range [X_i, X_i + D_i) on the number line, Robot j also gets activated and starts moving. This process is repeated recursively.

How many possible sets of robots remaining on the number line are there after Takahashi does the operation some number of times? Compute this count modulo 998244353, since it can be enormous.

Constraints

1 \leq N \leq 2 \times 10^5

-10^9 \leq X_i \leq 10^9

1 \leq D_i \leq 10^9

X_i \neq X_j (i \neq j)

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
X_1 D_1
:
X_N D_N

Output

Print the number of possible sets of robots remaining on the number line, modulo 998244353.

Sample Input 1

2
1 5
3 3

Sample Output 1

3

There are three possible sets of robots remaining on the number line: \{1, 2\}, \{1\}, and \{\}.

These can be achieved as follows:

If Takahashi activates nothing, the robots \{1, 2\} will remain.

If Takahashi activates Robot 1, it will activate Robot 2 while moving, after which there will be no robots on the number line. This state can also be reached by activating Robot 2 and then Robot 1.

If Takahashi activates Robot 2 and finishes doing the operation, the robot \{1\} will remain.

Sample Input 2

3
6 5
-1 10
3 3

Sample Output 2

5

There are five possible sets of robots remaining on the number line: \{1, 2, 3\}, \{1, 2\}, \{2\}, \{2, 3\}, and \{\}.

Sample Input 3

4
7 10
-10 3
4 3
-4 3

Sample Output 3

16

None of the robots influences others.

Sample Input 4

20
-8 1
26 4
0 5
9 1
19 4
22 20
28 27
11 8
-3 20
-25 17
10 4
-18 27
24 28
-11 19
2 27
-2 18
-1 12
-24 29
31 29
29 7

Sample Output 4

110

Remember to print the count modulo 998244353.

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Runtime.CompilerServices;
using System.Text;
using System.Threading.Tasks;

namespace AtCorder
{
	public class Program
	{
		static void Main(string[] args)
		{
			var cin = new Scanner2();
			int n = cin.Int();
			var xdt = new Tuple<long, long>[n];
			for (int i = 0; i < n; i++) {
				long x = cin.Long();
				long d = cin.Long();
				xdt[i] = new Tuple<long, long>(x, d);
			}

			var xd = xdt.OrderBy(x => x.Item1).ToArray();

			var reach = new SegmentTree<int>(n, 0, (x, y) => Math.Max(x, y));
			for (int i = n - 1; i >= 0; i--) {
				if (i == n - 1) {
					reach[i] = i;
				} else {
					long dd = xd[i].Item1 + xd[i].Item2;

					int ok = i;
					int ng = n;
					while (ng - ok > 1) {
						int mid = (ok + ng) / 2;
						if (xd[mid].Item1 < dd) {
							ok = mid;
						} else {
							ng = mid;
						}
					}

					if (ok == i) {
						reach[i] = i;
					} else if (i + 1 == ok) {
						reach[i] = reach[ok];
					} else {
						reach[i] = reach.Query(i + 1, ok + 1);
					}
				}
			}
			
			ModInt.P = 998244353;
			var dp = new ModInt[n + 1];
			dp[0] = 1;

			for (int i = 0; i < n; i++) {
				if (reach[i] == i) {
					dp[i + 1] += dp[i] * 2;
				} else {
					dp[i + 1] += dp[i];
					dp[reach[i] + 1] += dp[i];
				}
			}

			ModInt ans = dp[n];
			Console.WriteLine(ans.Value);
		}

		class Range
		{
			public int Count { get; set; }
			public long Max { get; set; }
		}
	}

	public class SegmentTree<T>
	{
		private readonly int n_;
		private readonly T unit_;
		private readonly T[] tree_;
		private readonly Func<T, T, T> merge_;

		public int Count { get; }
		public T Top => tree_[1];

		public SegmentTree(int count, T unit, Func<T, T, T> merge)
		{
			merge_ = merge;
			unit_ = unit;

			Count = count;
			n_ = 1;
			while (n_ < count) {
				n_ <<= 1;
			}

			tree_ = new T[n_ << 1];
			for (int i = 0; i < tree_.Length; i++) {
				tree_[i] = unit;
			}
		}

		public SegmentTree(T[] src, T max, Func<T, T, T> merge)
			: this(src.Length, max, merge)
		{
			for (int i = 0; i < n_; ++i) {
				tree_[i + n_] = src[i];
			}

			for (int i = n_ - 1; i > 0; --i) {
				tree_[i] = merge_(tree_[i << 1], tree_[(i << 1) + 1]);
			}
		}

		public T this[int index]
		{
			get { return tree_[index + n_]; }
			set { Update(index, value); }
		}

		public void Update(int index, T val)
		{
			if (index >= Count) {
				return;
			}

			index += n_;
			tree_[index] = val;
			index >>= 1;
			while (index != 0) {
				tree_[index] = merge_(tree_[index << 1], tree_[(index << 1) + 1]);
				index >>= 1;
			}
		}

		public T Query(int left, int right)
		{
			if (left > right || right < 0 || left >= Count) {
				return unit_;
			}

			int l = left + n_;
			int r = right + n_;
			T valL = unit_;
			T valR = unit_;
			while (l < r) {
				if ((l & 1) != 0) {
					valL = merge_(valL, tree_[l]);
					++l;
				}
				if ((r & 1) != 0) {
					--r;
					valR = merge_(tree_[r], valR);
				}

				l >>= 1;
				r >>= 1;
			}

			return merge_(valL, valR);
		}
	}

	public struct ModInt
	{
		public static long P { get; set; } = (long)1e9 + 7;

		public static ModInt Pow(ModInt value, long k)
		{
			return Pow(value.Value, k);
		}

		public static ModInt Pow(long value, long k)
		{
			long ret = 1;
			for (k %= P - 1; k > 0; k >>= 1, value = value * value % P) {
				if ((k & 1) == 1) {
					ret = ret * value % P;
				}
			}
			return new ModInt(ret);
		}

		public static ModInt Inverse(ModInt value)
		{
			return Pow(value, P - 2);
		}

		public long Value;

		public ModInt(long value)
		{
			value %= P;
			if (value < 0) {
				value += P;
			}

			Value = value;
		}

		public static ModInt operator +(ModInt lhs, ModInt rhs)
		{
			lhs.Value += rhs.Value;
			if (lhs.Value >= P) {
				lhs.Value -= P;
			}
			return lhs;
		}

		public static ModInt operator -(ModInt lhs, ModInt rhs)
		{
			lhs.Value -= rhs.Value;
			if (lhs.Value < 0) {
				lhs.Value += P;
			}

			return lhs;
		}

		public static ModInt operator *(ModInt lhs, ModInt rhs)
		{
			return new ModInt(lhs.Value * rhs.Value % P);
		}
		public static ModInt operator /(ModInt lhs, ModInt rhs)
		{
			long exp = P - 2;
			while (exp > 0) {
				if (exp % 2 > 0) {
					lhs *= rhs;
				}

				rhs *= rhs;
				exp /= 2;
			}

			return lhs;
		}

		public static implicit operator ModInt(long n)
		{
			n %= P;
			if (n < 0) {
				n += P;
			}

			return new ModInt(n);
		}

		public override string ToString()
		{
			return Value.ToString();
		}
	}

	public class Scanner2
	{
		private readonly char[] delimiter_ = new char[] { ' ' };
		private readonly string filePath_;
		private readonly Func<string> reader_;
		private string[] buf_;
		private int index_;

		public Scanner2(string file = "")
		{
			if (string.IsNullOrWhiteSpace(file)) {
				reader_ = Console.ReadLine;
			} else {
				filePath_ = file;
				var fs = new StreamReader(file);
				reader_ = fs.ReadLine;
			}
			buf_ = new string[0];
			index_ = 0;
		}

		public string Next()
		{
			if (index_ < buf_.Length) {
				return buf_[index_++];
			}

			string st = reader_();
			while (st == "") {
				st = reader_();
			}

			buf_ = st.Split(delimiter_, StringSplitOptions.RemoveEmptyEntries);
			if (buf_.Length == 0) {
				return Next();
			}

			index_ = 0;
			return buf_[index_++];
		}

		public int Int() => int.Parse(Next());
		public long Long() => long.Parse(Next());
		public double Double() => double.Parse(Next());

		public int[] ArrayInt(int N, int add = 0)
		{
			int[] Array = new int[N];
			for (int i = 0; i < N; i++) {
				Array[i] = Int() + add;
			}
			return Array;
		}

		public long[] ArrayLong(int N, long add = 0)
		{
			long[] Array = new long[N];
			for (int i = 0; i < N; i++) {
				Array[i] = Long() + add;
			}
			return Array;
		}

		public double[] ArrayDouble(int N, double add = 0)
		{
			double[] Array = new double[N];
			for (int i = 0; i < N; i++) {
				Array[i] = Double() + add;
			}
			return Array;
		}

		public void Save(string text)
		{
			if (string.IsNullOrWhiteSpace(filePath_)) {
				return;
			}

			File.WriteAllText(filePath_ + "_output.txt", text);
		}
	}
}