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.Collections;
using System.Collections.Generic;
using System.Diagnostics;
using System.Globalization;
using System.IO;
using System.Text;
using System.Linq;

using E = System.Linq.Enumerable;
using System.Threading;

internal partial class Solver {
    public void Run() {
        var n = ni();
        var q = ni();
        ModInt.SetMod998244353();
        var seg = new SegDef().CreateLazySegmentTree();
        seg.Build(n, v => new P { Sum = 1, Length = 1 });

        //cout.WriteLine(seg.Query(0, n).Sum);
        for (int _ = 0; _ < q; _++) {
            var l = ni() - 1;
            var r = ni() - 1;
            var d = ni();
            seg.LazyUpdate(l, r + 1, new Q { Value = d });
            cout.WriteLine(seg.Query(0, n).Sum);
        }
    }
}

public struct P {
    public ModInt Sum;
    public int Length;
}

public struct Q {
    public int? Value;
}

public class SegDef : ILazySegmentTreeDefinition<P, Q> {
    private ModInt[] ones = new ModInt[200010];
    private ModInt[] tens = new ModInt[200010];

    public SegDef() {
        ones[1] = 1;
        tens[0] = 1;
        for (int i = 2; i < ones.Length; i++) {
            ones[i] = ones[i - 1] * 10 + 1;
        }
        for (int i = 1; i < tens.Length; i++) {
            tens[i] = tens[i - 1] * 10;
        }
    }


    public P Identity => new P();

    public Q OperatorIdentity => new Q { };

    public P Apply(P monoid, int begin, int end, Q operation) {
        if (operation.Value.HasValue) {
            return new P { Sum = operation.Value.Value * ones[end - begin], Length = end - begin };
        } else {
            return monoid;
        }
    }

    public P Merge(P left, P right) {
        return new P { Sum = left.Sum * tens[right.Length] + right.Sum, Length = left.Length + right.Length };
    }

    public Q MergeOperator(Q current, Q append) {
        return new Q { Value = append.Value ?? current.Value };
    }
}


public partial struct ModInt : IEquatable<ModInt> {
    private static int mod = 0;
    private long _value;

    public ModInt(long x) {
        _value = x;
        Normalize();
    }

    private static long RegularMod(long x, int mod) {
        if (x >= mod) {
            if (x < 2 * mod) {
                return x - mod;
            }

            return x % mod;
        }
        if (x >= 0) {
            return x;
        }

        x = mod - RegularMod(-x, mod);
        return x == mod ? 0 : x;
    }

    public static int SetModValue(int m) {
        return mod = m;
    }
    public static int SetMod998244353() { return SetModValue(998244353); }
    public static int SetMod1000000007() { return SetModValue(1000000007); }

    private void Normalize() {
        _value = RegularMod(_value, mod);
    }

    public override string ToString() {
        return _value.ToString(CultureInfo.InvariantCulture);
    }

    public int ToInt() {
        return (int)_value;
    }

    public static bool operator ==(ModInt c1, ModInt c2) {
        return c1._value == c2._value;
    }

    public static bool operator !=(ModInt c1, ModInt c2) {
        return !(c1 == c2);
    }

    public static ModInt operator +(ModInt x, ModInt y) {
        return new ModInt(x._value + y._value);
    }
    public static ModInt operator -(ModInt x, ModInt y) {
        return new ModInt(x._value - y._value);
    }
    public static ModInt operator -(ModInt x) {
        return new ModInt(-x._value);
    }
    public static ModInt operator *(ModInt x, ModInt y) {
        return new ModInt(x._value * y._value);
    }
    public static ModInt operator /(ModInt x, ModInt y) {
        return new ModInt(x._value * Inverse(y._value, mod));
    }
    public static ModInt operator ++(ModInt x) {
        return x + 1;
    }
    public static ModInt operator --(ModInt x) {
        return x - 1;
    }
    public static ModInt Pow(ModInt x, long n) {
        ModInt r = 1;
        while (n > 0) {
            if ((n & 1) != 0) {
                r *= x;
            }

            x *= x;
            n >>= 1;
        }
        return r;
    }
    private static long ExtendedGcd(long a, long b, out long x, out long y) {
        if (b == 0) {
            x = 1; y = 0;
            return a;
        } else {
            var d = ExtendedGcd(b, a % b, out y, out x);
            y -= a / b * x;
            return d;
        }
    }

    private static long Inverse(long a, long mod) {
        long x = 0, y = 0;
        if (ExtendedGcd(a, mod, out x, out y) == 1) {
            return (x + mod) % mod;
        } else {
            throw new Exception("Invalid inverse " + a + " " + mod);
        }
    }

    public static implicit operator ModInt(long x) {
        return new ModInt(x);
    }

    public override bool Equals(object obj) {
        if (obj == null) {
            return false;
        }
        return _value.Equals(((ModInt)obj)._value);
    }

    public override int GetHashCode() {
        return _value.GetHashCode();
    }

    public bool Equals(ModInt other) {
        return _value.Equals(other._value);
    }
    object ToDump() { return _value; }
}


public interface ILazySegmentTreeDefinition<TMonoid, TOperatorMonoid> {
    TMonoid Merge(TMonoid left, TMonoid right);
    TMonoid Apply(TMonoid monoid, int begin, int @end, TOperatorMonoid operation);
    TOperatorMonoid MergeOperator(TOperatorMonoid current, TOperatorMonoid append);

    TMonoid Identity { get; }
    TOperatorMonoid OperatorIdentity { get; }
}
public static class LazySegmentTreeExtension {
    public static LazySegmentTree<TMonoid, TOperatorMonoid> CreateLazySegmentTree<TMonoid, TOperatorMonoid>
        (this ILazySegmentTreeDefinition<TMonoid, TOperatorMonoid> lazySegmentTreeMonoidOperator) {
        return new LazySegmentTree<TMonoid, TOperatorMonoid>(
            lazySegmentTreeMonoidOperator.Merge,
            lazySegmentTreeMonoidOperator.Apply,
            lazySegmentTreeMonoidOperator.MergeOperator,
            lazySegmentTreeMonoidOperator.Identity,
            lazySegmentTreeMonoidOperator.OperatorIdentity
        );
    }

    public static bool Check<TMonoid, TOperatorMonoid>
        (this ILazySegmentTreeDefinition<TMonoid, TOperatorMonoid> lazySegmentTreeMonoidOperator, TMonoid m, TOperatorMonoid o1, TOperatorMonoid o2) {
        var r1 = lazySegmentTreeMonoidOperator.Apply(lazySegmentTreeMonoidOperator.Apply(m, 1, 2, o1), 1, 2, o2);
        var r2 = lazySegmentTreeMonoidOperator.Apply(m, 1, 2, lazySegmentTreeMonoidOperator.MergeOperator(o1, o2));
        return r1.Equals(r2);
    }
}

public sealed class LazySegmentTree<TMonoid, TOperatorMonoid> {
    private int Count;

    private TMonoid[] _node;
    private TOperatorMonoid[] _operators;
    private int[] _height;
    private int[] _begin, _end;
    private readonly TMonoid _identity;
    private readonly TOperatorMonoid _operatorIdentity;
    private readonly Func<TMonoid, TMonoid, TMonoid> _merge;
    private readonly Func<TMonoid, int, int, TOperatorMonoid, TMonoid> _apply;
    private readonly Func<TOperatorMonoid, TOperatorMonoid, TOperatorMonoid> _mergeOperator;
    private readonly EqualityComparer<TOperatorMonoid> _equilityComparer;

    public LazySegmentTree(
        Func<TMonoid, TMonoid, TMonoid> merge,
        Func<TMonoid, int, int, TOperatorMonoid, TMonoid> apply,
        Func<TOperatorMonoid, TOperatorMonoid, TOperatorMonoid> mergeOperator,
        TMonoid identity,
        TOperatorMonoid operatorIdentity) {
        _merge = merge;
        _apply = apply;
        _mergeOperator = mergeOperator;
        _identity = identity;
        _operatorIdentity = operatorIdentity;
        _equilityComparer = EqualityComparer<TOperatorMonoid>.Default;
        if (_equilityComparer.GetType().Name.Contains("ObjectEqualityComparer")) {
            //throw new Exception(string.Format("Implement IEquality<T> for {0}", typeof(TOperatorMonoid).Name));
        }
    }

    public void Build(IList<TMonoid> array) {
        Build(array.Count, i => array[i]);
    }

    public void Build(int n, Func<int, TMonoid> create) {
        Count = n;

        _node = new TMonoid[2 * Count];
        _operators = new TOperatorMonoid[2 * Count];
        _begin = new int[2 * Count];
        _end = new int[2 * Count];
        _height = new int[2 * Count];
        for (var i = 0; i < _node.Length; i++) {
            _node[i] = _identity;
            _operators[i] = _operatorIdentity;
        }

        for (var i = 0; i < n; i++) {
            _node[i + Count] = create(i);
            _begin[i + Count] = i;
            _end[i + Count] = i + 1;
        }

        for (var i = 2; i < _height.Length; i++) {
            _height[i] = _height[i >> 1] + 1;
        }

        for (var i = Count - 1; i > 0; i--) {
            _node[i] = _merge(_node[i << 1], _node[i << 1 | 1]);
            _begin[i] = _begin[i << 1];
            _end[i] = _end[i << 1 | 1];
        }
    }

    private void Propagate(int k) {
        if (_equilityComparer.Equals(_operators[k], _operatorIdentity)) return;
        int childL = k << 1, childR = childL | 1;
        _operators[childL] = _mergeOperator(_operators[childL], _operators[k]);
        _operators[childR] = _mergeOperator(_operators[childR], _operators[k]);
        _node[k] = Apply(k);
        _operators[k] = _operatorIdentity;
    }

    public TMonoid Query(int begin, int end) {
        TMonoid lv = _identity, rv = _identity;
        begin += Count;
        end += Count;
        TopDownOperators(begin, end - 1);
        for (int l = begin, r = end - 1; l <= r; l >>= 1, r >>= 1) {
            if ((l & 1) == 1) { lv = _merge(lv, Apply(l++)); }
            if ((r & 1) == 0) { rv = _merge(Apply(r--), rv); }
        }
        return _merge(lv, rv);
    }

    public void LazyUpdate(int begin, int end, TOperatorMonoid @operator) {
        begin += Count;
        end += Count;
        TopDownOperators(begin, end - 1);
        for (int l = begin, r = end - 1; l <= r; l >>= 1, r >>= 1) {
            if ((l & 1) == 1) { _operators[l] = _mergeOperator(_operators[l], @operator); l++; }
            if ((r & 1) == 0) { _operators[r] = _mergeOperator(_operators[r], @operator); r--; }
        }
        BottomUpMonoids(begin, end - 1);
    }

    private void TopDownOperators(int k) {
        for (var i = _height[k]; i > 0; i--) {
            Propagate(k >> i);
        }
    }

    private void TopDownOperators(int l, int r) {
        var lh = _height[l];
        var rh = _height[r];
        while (lh < rh) Propagate(r >> rh--);
        while (lh > rh) Propagate(l >> lh--);
        var h = lh;
        for (; h > 0; h--) {
            Propagate(l >> h);
            if ((l >> h) != (r >> h)) Propagate(r >> h);
        }
    }

    private TMonoid Apply(int k) {
        if (_equilityComparer.Equals(_operators[k], _operatorIdentity)) return _node[k];
        return _apply(_node[k], _begin[k], _end[k], _operators[k]);
    }

    private void BottomUpMonoids(int k) {
        while ((k >>= 1) > 0) {
            _node[k] = _merge(Apply(k << 1), Apply(k << 1 | 1));
        }
    }

    private void BottomUpMonoids(int l, int r) {
        l >>= 1;
        r >>= 1;
        while (l != r) {
            if (l < r) {
                _node[r] = _merge(Apply(r << 1), Apply(r << 1 | 1)); r >>= 1;
            } else {
                _node[l] = _merge(Apply(l << 1), Apply(l << 1 | 1)); l >>= 1;
            }
        }
        while (l > 0) { _node[l] = _merge(Apply(l << 1), Apply(l << 1 | 1)); l >>= 1; }
    }

    public TMonoid this[int index] {
        get {
            index += Count;
            TopDownOperators(index);
            return Apply(index);
        }
        set {
            index += Count;
            TopDownOperators(index);
            _node[index] = value;
            _operators[index] = _operatorIdentity;
            BottomUpMonoids(index);
        }
    }

    public void Diagonsis() {
        for (var i = 1; i < Count; i++) {
            Propagate(i);
            var ex = _merge(Apply(i << 1), Apply(i << 1 | 1));
            var ex2 = Apply(i);
            if (!ex2.Equals(ex)) throw new Exception();
        }
    }

}



// PREWRITEN CODE BEGINS FROM HERE

static public class StringExtensions {
    static public string JoinToString<T>(this IEnumerable<T> source, string separator = " ") {
        return string.Join(separator, source);
    }
}

internal partial class Solver : Scanner {
    static readonly int? StackSizeInMebiByte = null; //50;
    public static void StartAndJoin(Action action, int maxStackSize) {
        var thread = new Thread(new ThreadStart(action), maxStackSize);
        thread.Start();
        thread.Join();
    }

    public static void Main() {
#if LOCAL
        byte[] inputBuffer = new byte[1000000];
        var inputStream = Console.OpenStandardInput(inputBuffer.Length);
        using (var reader = new StreamReader(inputStream, Console.InputEncoding, false, inputBuffer.Length)) {
            Console.SetIn(reader);
            new Solver(Console.In, Console.Out).Run();
        }
#else
        Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false });
        if (StackSizeInMebiByte.HasValue) {
            StartAndJoin(() => new Solver(Console.In, Console.Out).Run(), StackSizeInMebiByte.Value * 1024 * 1024);
        } else {
            new Solver(Console.In, Console.Out).Run();
        }
        Console.Out.Flush();
#endif
    }

#pragma warning disable IDE0052
    private readonly TextReader cin;
    private readonly TextWriter cout;
    private readonly TextWriter cerr;
#pragma warning restore IDE0052

    public Solver(TextReader reader, TextWriter writer)
        : base(reader) {
        cin = reader;
        cout = writer;
        cerr = Console.Error;
    }

    public Solver(string input, TextWriter writer)
        : this(new StringReader(input), writer) {
    }

#pragma warning disable IDE1006
#pragma warning disable IDE0051
    private int ni() { return NextInt(); }
    private int[] ni(int n) { return NextIntArray(n); }
    private long nl() { return NextLong(); }
    private long[] nl(int n) { return NextLongArray(n); }
    private double nd() { return NextDouble(); }
    private double[] nd(int n) { return NextDoubleArray(n); }
    private string ns() { return Next(); }
    private string[] ns(int n) { return NextArray(n); }
#pragma warning restore IDE1006
#pragma warning restore IDE0051
}

#if DEBUG
internal static class LinqPadExtension {
    public static string TextDump<T>(this T obj) {
        if (obj is IEnumerable) return (obj as IEnumerable).Cast<object>().JoinToString().Dump();
        else return obj.ToString().Dump();
    }
    public static T Dump<T>(this T obj) {
        return LINQPad.Extensions.Dump(obj);
    }
}
#endif

public class Scanner {
    private readonly TextReader Reader;
    private readonly CultureInfo ci = CultureInfo.InvariantCulture;

    private readonly char[] buffer = new char[2 * 1024];
    private int cursor = 0, length = 0;
    private string Token;
    private readonly StringBuilder sb = new StringBuilder(1024);

    public Scanner()
        : this(Console.In) {
    }

    public Scanner(TextReader reader) {
        Reader = reader;
    }

    public int NextInt() { return checked((int)NextLong()); }
    public long NextLong() {
        var s = Next();
        long r = 0;
        int i = 0;
        bool negative = false;
        if (s[i] == '-') {
            negative = true;
            i++;
        }
        for (; i < s.Length; i++) {
            r = r * 10 + (s[i] - '0');
#if DEBUG
            if (!char.IsDigit(s[i])) throw new FormatException();
#endif
        }
        return negative ? -r : r;
    }
    public double NextDouble() { return double.Parse(Next(), ci); }
    public string[] NextArray(int size) {
        string[] array = new string[size];
        for (int i = 0; i < size; i++) {
            array[i] = Next();
        }

        return array;
    }
    public int[] NextIntArray(int size) {
        int[] array = new int[size];
        for (int i = 0; i < size; i++) {
            array[i] = NextInt();
        }

        return array;
    }

    public long[] NextLongArray(int size) {
        long[] array = new long[size];
        for (int i = 0; i < size; i++) {
            array[i] = NextLong();
        }

        return array;
    }

    public double[] NextDoubleArray(int size) {
        double[] array = new double[size];
        for (int i = 0; i < size; i++) {
            array[i] = NextDouble();
        }

        return array;
    }

    public string Next() {
        if (Token == null) {
            if (!StockToken()) {
                throw new Exception();
            }
        }
        var token = Token;
        Token = null;
        return token;
    }

    public bool HasNext() {
        if (Token != null) {
            return true;
        }

        return StockToken();
    }

    private bool StockToken() {
        while (true) {
            sb.Clear();
            while (true) {
                if (cursor >= length) {
                    cursor = 0;
                    if ((length = Reader.Read(buffer, 0, buffer.Length)) <= 0) {
                        break;
                    }
                }
                var c = buffer[cursor++];
                if (33 <= c && c <= 126) {
                    sb.Append(c);
                } else {
                    if (sb.Length > 0) break;
                }
            }

            if (sb.Length > 0) {
                Token = sb.ToString();
                return true;
            }

            return false;
        }
    }
}