Problem:
Score : 500 points

Problem Statement

You have a string S of length N.
Initially, all characters in S are 1s.

You will perform queries Q times.
In the i-th query, you are given two integers L_i, R_i and a character D_i (which is a digit).
Then, you must replace all characters from the L_i-th to the R_i-th (inclusive) with D_i.

After each query, read the string S as a decimal integer, and print its value modulo 998,244,353.

Constraints

1 \leq N, Q \leq 200,000

1 \leq L_i \leq R_i \leq N

1 \leq D_i \leq 9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N Q
L_1 R_1 D_1
:
L_Q R_Q D_Q

Output

Print Q lines.
In the i-th line print the value of S after the i-th query, modulo 998,244,353.

Sample Input 1

8 5
3 6 2
1 4 7
3 8 3
2 2 2
4 5 1

Sample Output 1

11222211
77772211
77333333
72333333
72311333

Sample Input 2

200000 1
123 456 7

Sample Output 2

641437905

Don't forget to take the modulo.

Solution in C# (.NET Core 3.1.201) (judge verdict: Time Limit Exceeded)

using System;
using System.IO;
using System.Linq;
using CompLib.Util;
using System.Threading;
using CompLib.Collections.Generic;
using CompLib.Mathematics;

public class Program
{
    public void Solve()
    {
        var sc = new Scanner();
        int n = sc.NextInt();
        int q = sc.NextInt();
        var ar = new (ModInt num, int len)[n];
        for (int i = 0; i < n; i++)
        {
            ar[i] = (1, 1);
        }

        var lst = new LazySegmentTreeACL<(ModInt num, int len), (ModInt num, bool f)>(
            ar,
            (x, y) => (x.num * ModInt.Pow(10, y.len) + y.num, x.len + y.len),
            (0, 0),
            (f, x) => f.f ? (((ModInt.Pow(10, x.len) - 1) * f.num) * ModInt.Inverse(9), x.len) : x,
            (f, g) => f.f ? f : g.f ? g : (0, false),
            (0, false));

        Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) {AutoFlush = false});
        for (int i = 0; i < q; i++)
        {
            int l = sc.NextInt() - 1;
            int r = sc.NextInt();
            int d = sc.NextInt();
            lst.Apply(l, r, (d, true));

            Console.WriteLine(lst.All().num);
        }

        Console.Out.Flush();
    }

    public static void Main(string[] args) => new Program().Solve();
    // public static void Main(string[] args) => new Thread(new Program().Solve, 1 << 27).Start();
}

// https://bitbucket.org/camypaper/complib
namespace CompLib.Mathematics
{
    #region ModInt

    /// <summary>
    /// [0,<see cref="Mod"/>) までの値を取るような数
    /// </summary>
    public struct ModInt
    {
        /// <summary>
        /// 剰余を取る値．
        /// </summary>
        // public const long Mod = (int) 1e9 + 7;
        public const long Mod = 998244353;

        /// <summary>
        /// 実際の数値．
        /// </summary>
        public long num;

        /// <summary>
        /// 値が <paramref name="n"/> であるようなインスタンスを構築します．
        /// </summary>
        /// <param name="n">インスタンスが持つ値</param>
        /// <remarks>パフォーマンスの問題上，コンストラクタ内では剰余を取りません．そのため，<paramref name="n"/> ∈ [0,<see cref="Mod"/>) を満たすような <paramref name="n"/> を渡してください．このコンストラクタは O(1) で実行されます．</remarks>
        public ModInt(long n)
        {
            num = n;
        }

        /// <summary>
        /// このインスタンスの数値を文字列に変換します．
        /// </summary>
        /// <returns>[0,<see cref="Mod"/>) の範囲内の整数を 10 進表記したもの．</returns>
        public override string ToString()
        {
            return num.ToString();
        }

        public static ModInt operator +(ModInt l, ModInt r)
        {
            l.num += r.num;
            if (l.num >= Mod) l.num -= Mod;
            return l;
        }

        public static ModInt operator -(ModInt l, ModInt r)
        {
            l.num -= r.num;
            if (l.num < 0) l.num += Mod;
            return l;
        }

        public static ModInt operator *(ModInt l, ModInt r)
        {
            return new ModInt(l.num * r.num % Mod);
        }

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

        /// <summary>
        /// 与えられた 2 つの数値からべき剰余を計算します．
        /// </summary>
        /// <param name="v">べき乗の底</param>
        /// <param name="k">べき指数</param>
        /// <returns>繰り返し二乗法により O(N log N) で実行されます．</returns>
        public static ModInt Pow(ModInt v, long k)
        {
            return Pow(v.num, k);
        }

        /// <summary>
        /// 与えられた 2 つの数値からべき剰余を計算します．
        /// </summary>
        /// <param name="v">べき乗の底</param>
        /// <param name="k">べき指数</param>
        /// <returns>繰り返し二乗法により O(N log N) で実行されます．</returns>
        public static ModInt Pow(long v, long k)
        {
            long ret = 1;
            for (k %= Mod - 1; k > 0; k >>= 1, v = v * v % Mod)
                if ((k & 1) == 1)
                    ret = ret * v % Mod;
            return new ModInt(ret);
        }

        /// <summary>
        /// 与えられた数の逆元を計算します．
        /// </summary>
        /// <param name="v">逆元を取る対象となる数</param>
        /// <returns>逆元となるような値</returns>
        /// <remarks>法が素数であることを仮定して，フェルマーの小定理に従って逆元を O(log N) で計算します．</remarks>
        public static ModInt Inverse(ModInt v)
        {
            return Pow(v, Mod - 2);
        }
    }

    #endregion

    #region Binomial Coefficient

    public class BinomialCoefficient
    {
        public ModInt[] fact, ifact;

        public BinomialCoefficient(int n)
        {
            fact = new ModInt[n + 1];
            ifact = new ModInt[n + 1];
            fact[0] = 1;
            for (int i = 1; i <= n; i++)
                fact[i] = fact[i - 1] * i;
            ifact[n] = ModInt.Inverse(fact[n]);
            for (int i = n - 1; i >= 0; i--)
                ifact[i] = ifact[i + 1] * (i + 1);
            ifact[0] = ifact[1];
        }

        public ModInt this[int n, int r]
        {
            get
            {
                if (n < 0 || n >= fact.Length || r < 0 || r > n) return 0;
                return fact[n] * ifact[n - r] * ifact[r];
            }
        }

        public ModInt RepeatedCombination(int n, int k)
        {
            if (k == 0) return 1;
            return this[n + k - 1, k];
        }
    }

    #endregion
}


namespace CompLib.Collections.Generic
{
    using System;
    using System.Diagnostics;

    /// <summary>
    /// 長さnの配列の区間演算、区間更新ができるデータ構造
    /// </summary>
    /// <typeparam name="S">モノイドの型</typeparam>
    /// <typeparam name="F">写像の型</typeparam>
    public class LazySegmentTreeACL<S, F>
    {
        private readonly int _n;
        private readonly int _size;
        private int _log;

        private readonly S[] _d;
        private readonly F[] _lz;

        private readonly Func<S, S, S> _op;
        private readonly S _e;
        private readonly Func<F, S, S> _mapping;
        private readonly Func<F, F, F> _composition;
        private readonly F _id;

        /// <param name="n">サイズ</param>
        /// <param name="op">区間演算</param>
        /// <param name="e">Sの単位元</param>
        /// <param name="mapping">関数f(x)</param>
        /// <param name="composition">f*g, f(g(x))</param>
        /// <param name="id">f(x) = xとなるf (恒等写像)</param>
        public LazySegmentTreeACL(int n, Func<S, S, S> op, S e, Func<F, S, S> mapping, Func<F, F, F> composition, F id)
        {
            _n = n;
            _op = op;
            _e = e;
            _mapping = mapping;
            _composition = composition;
            _id = id;
            _size = 1;
            _log = 0;
            while (_size < _n)
            {
                _size <<= 1;
                _log++;
            }

            _d = new S[2 * _size];
            for (int i = 0; i < 2 * _size; i++)
            {
                _d[i] = _e;
            }

            _lz = new F[_size];
            for (int i = 0; i < _size; i++)
            {
                _lz[i] = _id;
            }
        }

        /// <param name="v">元配列</param>
        /// <param name="op">区間演算</param>
        /// <param name="e">Sの単位元</param>
        /// <param name="mapping">関数f(x)</param>
        /// <param name="composition">fの積</param>
        /// <param name="id">f(x) = xとなるf (恒等写像)</param>
        public LazySegmentTreeACL(S[] v, Func<S, S, S> op, S e, Func<F, S, S> mapping, Func<F, F, F> composition, F id)
        {
            _n = v.Length;
            _op = op;
            _e = e;
            _mapping = mapping;
            _composition = composition;
            _id = id;
            _size = 1;
            _log = 0;
            while (_size < _n)
            {
                _size <<= 1;
                _log++;
            }

            _d = new S[2 * _size];
            for (int i = 0; i < _n; i++)
            {
                _d[i + _size] = v[i];
            }

            for (int i = _n; i < _size; i++)
            {
                _d[i + _size] = _e;
            }

            for (int i = _size - 1; i >= 1; i--)
            {
                Update(i);
            }

            _lz = new F[_size];
            for (int i = 0; i < _size; i++)
            {
                _lz[i] = _id;
            }
        }

        /// <summary>
        /// A[p]にxを代入 O(log n)
        /// </summary>
        /// <param name="p"></param>
        /// <param name="x"></param>
        public void Set(int p, S x)
        {
            Debug.Assert(0 <= p && p < _n);
            p += _size;
            for (int i = _log; i >= 1; i--) Push(p >> i);
            _d[p] = x;
            for (int i = 1; i <= _log; i++) Update(p >> i);
        }

        /// <summary>
        /// A[p] を返す O(log n)
        /// </summary>
        /// <param name="p"></param>
        /// <returns></returns>
        public S Get(int p)
        {
            Debug.Assert(0 <= p && p < _n);
            p += _size;
            for (int i = _log; i >= 1; i--) Push(p >> i);
            return _d[p];
        }

        /// <summary>
        /// op(A[l,r))を計算します O(log n)
        /// </summary>
        /// <param name="l"></param>
        /// <param name="r"></param>
        /// <returns></returns>
        public S Query(int l, int r)
        {
            Debug.Assert(0 <= l && l <= r && r <= _n);
            if (l == r) return _e;
            l += _size;
            r += _size;
            for (int i = _log; i >= 1; i--)
            {
                if (((l >> i) << i) != l) Push(l >> i);
                if (((r >> i) << i) != r) Push(r >> i);
            }

            S sml = _e, smr = _e;
            while (l < r)
            {
                if ((l & 1) != 0) sml = _op(sml, _d[l++]);
                if ((r & 1) != 0) smr = _op(_d[--r], smr);
                l >>= 1;
                r >>= 1;
            }

            return _op(sml, smr);
        }

        /// <summary>
        /// op(A)を計算します O(1)
        /// </summary>
        /// <returns></returns>
        public S All()
        {
            return _d[1];
        }

        /// <summary>
        /// A[p]にf(A[p])を代入します O(log n)
        /// </summary>
        /// <param name="p"></param>
        /// <param name="f"></param>
        public void Apply(int p, F f)
        {
            Debug.Assert(0 <= p && p < _n);
            p += _size;
            for (int i = _log; i >= 1; i--) Push(p >> i);
            _d[p] = _mapping(f, _d[p]);
            for (int i = 1; i <= _log; i++) Update(p >> i);
        }

        /// <summary>
        /// i = l,l+1,...,r-1について A[i]にf(A[i])を代入します O(log n)
        /// </summary>
        /// <param name="l"></param>
        /// <param name="r"></param>
        /// <param name="f"></param>
        public void Apply(int l, int r, F f)
        {
            Debug.Assert(0 <= l && l <= r && r <= _n);
            if (l == r) return;

            l += _size;
            r += _size;

            for (int i = _log; i >= 1; i--)
            {
                if (((l >> i) << i) != l) Push(l >> i);
                if (((r >> i) << i) != r) Push((r - 1) >> i);
            }

            {
                int l2 = l, r2 = r;
                while (l < r)
                {
                    if ((l & 1) > 0) AllApply(l++, f);
                    if ((r & 1) > 0) AllApply(--r, f);
                    l >>= 1;
                    r >>= 1;
                }

                l = l2;
                r = r2;
            }

            for (int i = 1; i <= _log; i++)
            {
                if (((l >> i) << i) != l) Update(l >> i);
                if (((r >> i) << i) != r) Update((r - 1) >> i);
            }
        }

        /// <summary>
        /// g(op(A[l,r))) = true となる最大のrを探します O(log n)
        /// </summary>
        /// <param name="l"></param>
        /// <param name="g"></param>
        /// <returns></returns>
        public int MaxRight(int l, Func<S, bool> g)
        {
            Debug.Assert(0 <= l && l <= _n);
#if DEBUG
            Debug.Assert(g(_e));
#endif
            if (l == _n) return _n;
            l += _size;
            for (int i = _log; i >= 1; i--) Push(l >> i);
            S sm = _e;
            do
            {
                while (l % 2 == 0) l >>= 1;
                if (!g(_op(sm, _d[l])))
                {
                    while (l < _size)
                    {
                        Push(l);
                        l = (2 * l);
                        if (g(_op(sm, _d[l])))
                        {
                            sm = _op(sm, _d[l]);
                            l++;
                        }
                    }

                    return l - _size;
                }

                sm = _op(sm, _d[l]);
                l++;
            } while ((l & -l) != l);

            return _n;
        }

        /// <summary>
        /// g(op(A[l,r))) = trueとなる最小のlを探します O(log n)
        /// </summary>
        /// <param name="r"></param>
        /// <param name="g"></param>
        /// <returns></returns>
        public int MinLeft(int r, Func<S, bool> g)
        {
            Debug.Assert(0 <= r && r <= _n);
#if DEBUG
            Debug.Assert(g(_e));
#endif
            if (r == 0) return 0;
            r += _size;
            for (int i = _log; i >= 1; i--) Push((r - 1) >> i);
            S sm = _e;
            do
            {
                r--;
                while (r > 1 && (r % 2) != 0) r >>= 1;
                if (!g(_op(_d[r], sm)))
                {
                    while (r < _size)
                    {
                        Push(r);
                        r = (2 * r + 1);
                        if (g(_op(_d[r], sm)))
                        {
                            sm = _op(_d[r], sm);
                            r--;
                        }
                    }

                    return r + 1 - _size;
                }

                sm = _op(_d[r], sm);
            } while ((r & -r) != r);

            return 0;
        }

        public S this[int p]
        {
            get { return Get(p); }
            set { Set(p, value); }
        }

        private void Update(int k)
        {
            _d[k] = _op(_d[2 * k], _d[2 * k + 1]);
        }

        private void AllApply(int k, F f)
        {
            _d[k] = _mapping(f, _d[k]);
            if (k < _size) _lz[k] = _composition(f, _lz[k]);
        }

        private void Push(int k)
        {
            AllApply(2 * k, _lz[k]);
            AllApply(2 * k + 1, _lz[k]);
            _lz[k] = _id;
        }
    }
}


namespace CompLib.Util
{
    using System;
    using System.Linq;

    class Scanner
    {
        private string[] _line;
        private int _index;
        private const char Separator = ' ';

        public Scanner()
        {
            _line = new string[0];
            _index = 0;
        }

        public string Next()
        {
            if (_index >= _line.Length)
            {
                string s;
                do
                {
                    s = Console.ReadLine();
                } while (s.Length == 0);

                _line = s.Split(Separator);
                _index = 0;
            }

            return _line[_index++];
        }

        public string ReadLine()
        {
            _index = _line.Length;
            return Console.ReadLine();
        }

        public int NextInt() => int.Parse(Next());
        public long NextLong() => long.Parse(Next());
        public double NextDouble() => double.Parse(Next());
        public decimal NextDecimal() => decimal.Parse(Next());
        public char NextChar() => Next()[0];
        public char[] NextCharArray() => Next().ToCharArray();

        public string[] Array()
        {
            string s = Console.ReadLine();
            _line = s.Length == 0 ? new string[0] : s.Split(Separator);
            _index = _line.Length;
            return _line;
        }

        public int[] IntArray() => Array().Select(int.Parse).ToArray();
        public long[] LongArray() => Array().Select(long.Parse).ToArray();
        public double[] DoubleArray() => Array().Select(double.Parse).ToArray();
        public decimal[] DecimalArray() => Array().Select(decimal.Parse).ToArray();
    }
}