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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

// Optimise
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
using namespace __gnu_pbds;

// #define MULTI_TEST
#ifdef LOCAL
#include "/home/shahraaz/bin/debug.h"
#else
#define db(...)
#define pc(...)
#endif

#define f first
#define s second
#define pb push_back
#define all(v) v.begin(), v.end()
auto TimeStart = chrono::steady_clock::now();
auto seed = TimeStart.time_since_epoch().count();
std::mt19937 rng(seed);
using ll = long long;
template <typename T>
using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
template <typename T>
using Random = std::uniform_int_distribution<T>;

const int NAX = 2e5 + 5, MOD = 998244353;

struct Node
{
    pair<int, int> val;
    Node(int value = -1, int idx = -1)
    {
        val = make_pair(value, idx);
    }
    Node operator+(const Node &rhs)
    {
        Node a = *this;
        a.val = max(a.val, rhs.val);
        return a;
    }
};
// ostream &operator<<(ostream &out, const Node &p)
// {
//     out << p.val;
//     return out;
// }
// istream &operator>>(istream &in, Node &p)
// {
//     in >> p.val;
//     return in;
// }

struct Segtree
{
    vector<Node> Seg, Lazy;
    vector<Node> Base;
    vector<bool> isLazy;
    int n;
    Segtree(int n = 2e5)
    {
        this->n = n;
        Seg.resize(4 * n + 10);
        Lazy.resize(4 * n + 10);
        isLazy.resize(4 * n + 10);
    }
    void merge(Node &curr, Node &l, Node &r)
    {
        curr = l + r;
    }
    void propagate(int node, int L, int R)
    {
        if (isLazy[node])
        {
            isLazy[node] = false;
            Seg[node] = Seg[node] + Lazy[node];
            if (L != R)
            {
                Lazy[2 * node] = Lazy[2 * node] + Lazy[node];
                Lazy[2 * node + 1] = Lazy[2 * node + 1] + Lazy[node];
                isLazy[2 * node] = true;
                isLazy[2 * node + 1] = true;
            }
            Lazy[node] = Node();
        }
    }
    void build(int node, int start, int end)
    {
        if (start == end)
        {
            Seg[node] = Base[start];
            return;
        }
        int mid = (start + end) / 2;
        build(2 * node, start, mid);
        build(2 * node + 1, mid + 1, end);
        merge(Seg[node], Seg[2 * node], Seg[2 * node + 1]);
    }
    void build(vector<Node> &Arr)
    {
        Base = Arr;
        n = Arr.size();
        Seg.resize(4 * n + 10);
        Lazy.resize(4 * n + 10);
        isLazy.resize(4 * n + 10);
        build(1, 0, n - 1);
    }
    Node Query(int node, int start, int end, int qstart, int qend)
    {
        propagate(node, start, end);
        if (qend < start || qstart > end || start > end)
            return Node();
        if (qstart <= start && end <= qend)
            return Seg[node];
        int mid = (start + end) / 2;
        Node l = Query(2 * node, start, mid, qstart, qend);
        Node r = Query(2 * node + 1, mid + 1, end, qstart, qend);
        Node ret;
        merge(ret, l, r);
        return ret;
    }
    Node qQuery(int node, int start, int end, int pos)
    {
        propagate(node, start, end);
        if (start == end)
            return Seg[node];
        int mid = (start + end) / 2;
        if (pos <= mid)
            return qQuery(2 * node, start, mid, pos);
        return qQuery(2 * node + 1, mid + 1, end, pos);
    }
    void Update(int node, int start, int end, int qstart, int qend, Node val)
    {
        propagate(node, start, end);
        if (qend < start || qstart > end || start > end)
            return;
        if (qstart <= start && end <= qend)
        {
            isLazy[node] = true;
            Lazy[node] = val;
            propagate(node, start, end);
            return;
        }
        int mid = (start + end) / 2;
        Update(2 * node, start, mid, qstart, qend, val);
        Update(2 * node + 1, mid + 1, end, qstart, qend, val);
        merge(Seg[node], Seg[2 * node], Seg[2 * node + 1]);
    }
    void pUpdate(int node, int start, int end, int pos, Node val)
    {
        propagate(node, start, end);
        if (start == end)
        {
            isLazy[node] = true;
            Seg[node] = Node();
            Lazy[node] = val;
            propagate(node, start, end);
            return;
        }
        int mid = (start + end) / 2;
        if (pos <= mid)
            pUpdate(2 * node, start, mid, pos, val);
        else
            pUpdate(2 * node + 1, mid + 1, end, pos, val);
        merge(Seg[node], Seg[2 * node], Seg[2 * node + 1]);
    }
    Node query(int pos)
    {
        return qQuery(1, 0, n - 1, pos);
    }
    Node query(int left, int right)
    {
        return Query(1, 0, n - 1, left, right);
    }
    void update(int pos, Node val)
    {
        pUpdate(1, 0, n - 1, pos, val);
    }
    void update(int start, int end, Node val)
    {
        Update(1, 0, n - 1, start, end, val);
    }
};

const int kmod = 998244353;

int mul(int a, int b, int mod = kmod)
{
    return (long long)a * b % mod;
}

int add(int a, int b, int mod = kmod)
{
    a += b;
    if (a >= mod)
        a -= mod;
    return a;
}

int sub(int a, int b, int mod = kmod)
{
    a -= b;
    if (a < 0)
        a += mod;
    return a;
}

int dp[NAX][2];
class Solution
{
private:
public:
    Solution() {}
    ~Solution() {}
    void solveCase()
    {
        int n;
        cin >> n;
        vector<pair<int, int>> X(n);
        vector<int> xonly;
        for (auto &x : X)
        {
            cin >> x.f >> x.s;
        }
        for (size_t i = 0; i < n; i++)
            xonly.pb(X[i].f);
        sort(all(X));
        sort(all(xonly));
        dp[n - 1][0] = dp[n - 1][1] = 1;
        Segtree S(n + 1);
        S.update(n - 1, Node(X[n - 1].f + X[n - 1].s - 1, dp[n - 1][1]));
        for (int i = n - 2; i >= 0; i--)
        {
            dp[i][0] = add(dp[i + 1][0], dp[i + 1][1]);
            auto it = lower_bound(all(xonly), xonly[i] + X[i].s);
            if (it == xonly.begin())
            {
                dp[i][1] = add(dp[i + 1][0], dp[i + 1][1]);
            }
            else
            {
                --it;
                auto idx = it - xonly.begin();
                db(i, idx);
                if (idx == i)
                    dp[i][1] = add(dp[i + 1][0], dp[i + 1][1]);
                else
                {
                    auto q = S.query(i + 1, idx);
                    db(q.val);
                    if (q.val.f == -1)
                        dp[i][1] = add(dp[i + 1][0], dp[i + 1][1]);
                    else
                        dp[i][1] = q.val.s;
                }
            }
            S.update(i, Node(X[i].f + X[i].s - 1, dp[i][1]));
            db(i, dp[i][0], dp[i][1]);
        }
        cout << add(dp[0][0], dp[0][1]) << '\n';
    }
};

int32_t main()
{
#ifndef LOCAL
    ios_base::sync_with_stdio(0);
    cin.tie(0);
#endif
    int t = 1;
#ifdef MULTI_TEST
    cin >> t;
#endif
    Solution mySolver;
    for (int i = 1; i <= t; ++i)
    {
        mySolver.solveCase();
#ifdef TIME
        cerr << "Case #" << i << ": Time " << chrono::duration<double>(chrono::steady_clock::now() - TimeStart).count() << " s.\n";
        TimeStart = chrono::steady_clock::now();
#endif
    }
    return 0;
}