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: Accepted)

using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using static System.Math;
using System.Text;
using System.Threading;
using System.Globalization;
using System.Runtime.CompilerServices;
using Library;

namespace Program
{
    public static class ProblemE
    {
        static bool SAIKI = false;
        static public int numberOfRandomCases = 0;
        static public void MakeTestCase(List<string> _input, List<string> _output, ref Func<string[], bool> _outputChecker)
        {
        }
        static public void Solve()
        {
            var N = NN;
            var Q = NN;
            var LRD = Repeat(0, Q).Select(_ => new { L = NN - 1, R = NN - 1, D = NN }).ToArray();
            LIB_Mod._mod = 998244353;
            var seg = new LIB_LazySegTree<(LIB_Mod sum, LIB_Mod keta), long>(N, (0, 0), 0,
                (x, y) => (sum: x.sum + y.sum, keta: x.keta + y.keta),
                (x, y, c) => (sum: x.keta * y, x.keta),
                (x, y) => y
            );
            LIB_Mod keta = 1;
            for (var i = 0; i < N; i++)
            {
                seg[N - i - 1] = (keta, keta);
                keta *= 10;
            }
            foreach (var item in LRD)
            {
                seg.Update(item.L, item.R + 1, item.D);
                Console.WriteLine(seg.Query(0, N).sum);
            }
        }
        class Printer : StreamWriter
        {
            public override IFormatProvider FormatProvider { get { return CultureInfo.InvariantCulture; } }
            public Printer(Stream stream) : base(stream, new UTF8Encoding(false, true)) { base.AutoFlush = false; }
            public Printer(Stream stream, Encoding encoding) : base(stream, encoding) { base.AutoFlush = false; }
        }
        static LIB_FastIO fastio = new LIB_FastIODebug();
        static public void Main(string[] args) { if (args.Length == 0) { fastio = new LIB_FastIO(); Console.SetOut(new Printer(Console.OpenStandardOutput())); } if (SAIKI) { var t = new Thread(Solve, 134217728); t.Start(); t.Join(); } else Solve(); Console.Out.Flush(); }
        static long NN => fastio.Long();
        static double ND => fastio.Double();
        static string NS => fastio.Scan();
        static long[] NNList(long N) => Repeat(0, N).Select(_ => NN).ToArray();
        static double[] NDList(long N) => Repeat(0, N).Select(_ => ND).ToArray();
        static string[] NSList(long N) => Repeat(0, N).Select(_ => NS).ToArray();
        static long Count<T>(this IEnumerable<T> x, Func<T, bool> pred) => Enumerable.Count(x, pred);
        static IEnumerable<T> Repeat<T>(T v, long n) => Enumerable.Repeat<T>(v, (int)n);
        static IEnumerable<int> Range(long s, long c) => Enumerable.Range((int)s, (int)c);
        static IOrderedEnumerable<T> OrderByRand<T>(this IEnumerable<T> x) => Enumerable.OrderBy(x, _ => xorshift);
        static IOrderedEnumerable<T> OrderBy<T>(this IEnumerable<T> x) => Enumerable.OrderBy(x.OrderByRand(), e => e);
        static IOrderedEnumerable<T1> OrderBy<T1, T2>(this IEnumerable<T1> x, Func<T1, T2> selector) => Enumerable.OrderBy(x.OrderByRand(), selector);
        static IOrderedEnumerable<T> OrderByDescending<T>(this IEnumerable<T> x) => Enumerable.OrderByDescending(x.OrderByRand(), e => e);
        static IOrderedEnumerable<T1> OrderByDescending<T1, T2>(this IEnumerable<T1> x, Func<T1, T2> selector) => Enumerable.OrderByDescending(x.OrderByRand(), selector);
        static IOrderedEnumerable<string> OrderBy(this IEnumerable<string> x) => x.OrderByRand().OrderBy(e => e, StringComparer.OrdinalIgnoreCase);
        static IOrderedEnumerable<T> OrderBy<T>(this IEnumerable<T> x, Func<T, string> selector) => x.OrderByRand().OrderBy(selector, StringComparer.OrdinalIgnoreCase);
        static IOrderedEnumerable<string> OrderByDescending(this IEnumerable<string> x) => x.OrderByRand().OrderByDescending(e => e, StringComparer.OrdinalIgnoreCase);
        static IOrderedEnumerable<T> OrderByDescending<T>(this IEnumerable<T> x, Func<T, string> selector) => x.OrderByRand().OrderByDescending(selector, StringComparer.OrdinalIgnoreCase);
        static string Join<T>(this IEnumerable<T> x, string separator = "") => string.Join(separator, x);
        static uint xorshift { get { _xsi.MoveNext(); return _xsi.Current; } }
        static IEnumerator<uint> _xsi = _xsc();
        static IEnumerator<uint> _xsc() { uint x = 123456789, y = 362436069, z = 521288629, w = (uint)(DateTime.Now.Ticks & 0xffffffff); while (true) { var t = x ^ (x << 11); x = y; y = z; z = w; w = (w ^ (w >> 19)) ^ (t ^ (t >> 8)); yield return w; } }
    }
}
namespace Library {
    partial struct LIB_Mod : IEquatable<LIB_Mod>, IEquatable<long>
    {
        static public long _mod = 1000000007; long v;
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public LIB_Mod(long x)
        {
            if (x < _mod && x >= 0) v = x;
            else if ((v = x % _mod) < 0) v += _mod;
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static public implicit operator LIB_Mod(long x) => new LIB_Mod(x);
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static public implicit operator long(LIB_Mod x) => x.v;
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public void Add(LIB_Mod x) { if ((v += x.v) >= _mod) v -= _mod; }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public void Sub(LIB_Mod x) { if ((v -= x.v) < 0) v += _mod; }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public void Mul(LIB_Mod x) => v = (v * x.v) % _mod;
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public void Div(LIB_Mod x) => v = (v * Inverse(x.v)) % _mod;
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static public LIB_Mod operator +(LIB_Mod x, LIB_Mod y) { var t = x.v + y.v; return t >= _mod ? new LIB_Mod { v = t - _mod } : new LIB_Mod { v = t }; }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static public LIB_Mod operator -(LIB_Mod x, LIB_Mod y) { var t = x.v - y.v; return t < 0 ? new LIB_Mod { v = t + _mod } : new LIB_Mod { v = t }; }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static public LIB_Mod operator *(LIB_Mod x, LIB_Mod y) => x.v * y.v;
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static public LIB_Mod operator /(LIB_Mod x, LIB_Mod y) => x.v * Inverse(y.v);
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static public bool operator ==(LIB_Mod x, LIB_Mod y) => x.v == y.v;
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static public bool operator !=(LIB_Mod x, LIB_Mod y) => x.v != y.v;
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static public long Inverse(long x)
        {
            long b = _mod, r = 1, u = 0, t = 0;
            while (b > 0)
            {
                var q = x / b;
                t = u;
                u = r - q * u;
                r = t;
                t = b;
                b = x - q * b;
                x = t;
            }
            return r < 0 ? r + _mod : r;
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public bool Equals(LIB_Mod x) => v == x.v;
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public bool Equals(long x) => v == x;
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public override bool Equals(object x) => x == null ? false : Equals((LIB_Mod)x);
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public override int GetHashCode() => v.GetHashCode();
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public override string ToString() => v.ToString();
        static List<LIB_Mod> _fact = new List<LIB_Mod>() { 1 };
        static long _factm = _mod;
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static void B(long n)
        {
            if (_factm != _mod) _fact = new List<LIB_Mod>() { 1 };
            if (n >= _fact.Count)
                for (int i = _fact.Count; i <= n; ++i)
                    _fact.Add(_fact[i - 1] * i);
            _factm = _mod;
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static public LIB_Mod Comb(long n, long k)
        {
            B(n);
            if (n == 0 && k == 0) return 1;
            if (n < k || n < 0) return 0;
            return _fact[(int)n] / _fact[(int)(n - k)] / _fact[(int)k];
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static public LIB_Mod CombOK(long n, long k)
        {
            LIB_Mod ret = 1;
            for (var i = 0; i < k; i++) ret *= n - i;
            for (var i = 1; i <= k; i++) ret /= i;
            return ret;
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static public LIB_Mod Perm(long n, long k)
        {
            B(n);
            if (n == 0 && k == 0) return 1;
            if (n < k || n < 0) return 0;
            return _fact[(int)n] / _fact[(int)(n - k)];
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static public LIB_Mod KanzenPerm(long n) => Enumerable.Range(0, (int)n + 1).Aggregate((LIB_Mod)0, (a, e) => a + (1 - ((e & 1) << 1)) * LIB_Mod.Comb(n, e) * LIB_Mod.Perm(n - e, n - e));
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static public LIB_Mod Pow(LIB_Mod x, long y)
        {
            LIB_Mod a = 1;
            while (y != 0)
            {
                if ((y & 1) == 1) a.Mul(x);
                x.Mul(x);
                y >>= 1;
            }
            return a;
        }
    }
    class LIB_LazySegTree
    {
        static public LIB_LazySegTree<long, long> CreateRangeUpdateRangeMin(IEnumerable<long> init) => new LIB_LazySegTree<long, long>(init, long.MaxValue, long.MinValue + 100, Math.Min, (x, y, c) => y, (x, y) => y);
        static public LIB_LazySegTree<long, long> CreateRangeAddRangeMin(IEnumerable<long> init) => new LIB_LazySegTree<long, long>(init, long.MaxValue, 0, Math.Min, (x, y, c) => x + y, (x, y) => x + y);
        static public LIB_LazySegTree<long, long> CreateRangeUpdateRangeMax(IEnumerable<long> init) => new LIB_LazySegTree<long, long>(init, long.MinValue, long.MaxValue - 100, Math.Max, (x, y, c) => y, (x, y) => y);
        static public LIB_LazySegTree<long, long> CreateRangeAddRangeMax(IEnumerable<long> init) => new LIB_LazySegTree<long, long>(init, long.MinValue, 0, Math.Max, (x, y, c) => x + y, (x, y) => x + y);
        static public LIB_LazySegTree<long, long> CreateRangeUpdateRangeSum(IEnumerable<long> init) => new LIB_LazySegTree<long, long>(init, 0, long.MaxValue, (x, y) => x + y, (x, y, c) => y * c, (x, y) => y);
        static public LIB_LazySegTree<long, long> CreateRangeAddRangeSum(IEnumerable<long> init) => new LIB_LazySegTree<long, long>(init, 0, 0, (x, y) => x + y, (x, y, c) => x + y * c, (x, y) => x + y);
    }
    class LIB_LazySegTree<T, E> where E : IEquatable<E>
    {
        int n, height, sz;
        int[] rangeSz;
        T ti;
        E ei;
        Func<T, T, T> f;
        Func<T, E, int, T> g;
        Func<E, E, E> h;
        T[] dat;
        E[] laz;
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public LIB_LazySegTree(long _n, T _ti, E _ei, Func<T, T, T> _f, Func<T, E, int, T> _g, Func<E, E, E> _h)
        {
            n = 1; height = 0; sz = (int)_n;
            while (n < _n) { n <<= 1; ++height; }
            ti = _ti;
            ei = _ei;
            f = _f;
            g = _g;
            h = _h;
            dat = Enumerable.Repeat(ti, n << 1).ToArray();
            laz = Enumerable.Repeat(ei, n).ToArray();
            rangeSz = new int[n << 1];
            for (var i = 0; i < sz; i++) rangeSz[n + i] = 1;
            for (var i = n - 1; i > 0; i--)
            {
                rangeSz[i] = rangeSz[(i << 1) | 0] + rangeSz[(i << 1) | 1];
                dat[i] = f(dat[(i << 1) | 0], dat[(i << 1) | 1]);
            }
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public LIB_LazySegTree(IEnumerable<T> l, T _ti, E _ei, Func<T, T, T> _f, Func<T, E, int, T> _g, Func<E, E, E> _h) : this(l.Count(), _ti, _ei, _f, _g, _h)
        {
            var idx = 0;
            foreach (var item in l) dat[n + idx++] = item;
            for (var i = n - 1; i > 0; i--) dat[i] = f(dat[(i << 1) | 0], dat[(i << 1) | 1]);
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        void Apply(long i, ref E v)
        {
            if (v.Equals(ei)) return;
            dat[i] = g(dat[i], v, rangeSz[i]);
            if (i < n) laz[i] = h(laz[i], v);
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        void Up(long i) => dat[i] = f(dat[i << 1], dat[(i << 1) | 1]);
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        void Down(long i)
        {
            if (laz[i].Equals(ei)) return;
            var cl = i << 1;
            var cr = cl + 1;
            Apply(cl, ref laz[i]);
            Apply(cr, ref laz[i]);
            laz[i] = ei;
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        void Thrust(long i)
        {
            for (var j = height; j > 0; j--) Down(i >> j);
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        void Recalc(long i)
        {
            while ((i >>= 1) > 0) Up(i);
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public void Update(long l, long r, E v)
        {
            if (l == r) return;
            l += n;
            r += n;
            for (var i = height; i >= 1; --i)
            {
                if (((l >> i) << i) != l) Down(l >> i);
                if (((r >> i) << i) != r) Down((r - 1) >> i);
            }
            for (long li = l, ri = r; li < ri; li >>= 1, ri >>= 1)
            {
                if ((li & 1) == 1) { Apply(li, ref v); ++li; }
                if ((ri & 1) == 1) { --ri; Apply(ri, ref v); }
            }
            for (var i = 1; i <= height; ++i)
            {
                if (((l >> i) << i) != l) Up(l >> i);
                if (((r >> i) << i) != r) Up((r - 1) >> i);
            }
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public T Query(long l, long r)
        {
            if (l == r) return ti;
            l += n;
            r += n;
            for (var i = height; i >= 1; --i)
            {
                if (((l >> i) << i) != l) Down(l >> i);
                if (((r >> i) << i) != r) Down((r - 1) >> i);
            }
            var vl = ti; var vr = ti;
            for (long li = l, ri = r; li < ri; li >>= 1, ri >>= 1)
            {
                if ((li & 1) == 1) vl = f(vl, dat[li++]);
                if ((ri & 1) == 1) vr = f(dat[--ri], vr);
            }
            return f(vl, vr);
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        int FindToRight(int st, Func<T, bool> check, ref T acc, int k, int l, int r)
        {
            if (l + 1 == r)
            {
                acc = f(acc, dat[k]);
                return check(acc) ? k - n : sz;
            }
            Down(k);
            int m = (l + r) >> 1;
            if (m <= st) return FindToRight(st, check, ref acc, (k << 1) | 1, m, r);
            if (st <= l && !check(f(acc, dat[k])))
            {
                acc = f(acc, dat[k]);
                return sz;
            }
            int vl = FindToRight(st, check, ref acc, (k << 1) | 0, l, m);
            if (vl != sz) return vl;
            return FindToRight(st, check, ref acc, (k << 1) | 1, m, r);
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public int FindToRight(int st, Func<T, bool> check)
        {
            T acc = ti;
            return FindToRight(st, check, ref acc, 1, 0, n);
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        int FindToLeft(int st, Func<T, bool> check, ref T acc, int k, int l, int r)
        {
            if (l + 1 == r)
            {
                acc = f(dat[k], acc);
                return check(acc) ? k - n : -1;
            }
            Down(k);
            int m = (l + r) >> 1;
            if (m > st) return FindToLeft(st, check, ref acc, (k << 1) | 0, l, m);
            if (st >= r - 1 && !check(f(dat[k], acc)))
            {
                acc = f(dat[k], acc);
                return -1;
            }
            int vr = FindToLeft(st, check, ref acc, (k << 1) | 1, m, r);
            if (vr != -1) return vr;
            return FindToLeft(st, check, ref acc, (k << 1) | 0, l, m);
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public int FindToLeft(int st, Func<T, bool> check)
        {
            T acc = ti;
            return FindToLeft(st, check, ref acc, 1, 0, n);
        }
        public T this[long idx]
        {
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            get { Thrust(idx += n); return dat[idx]; }
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            set { Thrust(idx += n); dat[idx] = value; Recalc(idx); }
        }
    }
    class LIB_FastIO
    {
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public LIB_FastIO() { str = Console.OpenStandardInput(); }
        readonly Stream str;
        readonly byte[] buf = new byte[2048];
        int len, ptr;
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        byte read()
        {
            if (ptr >= len)
            {
                ptr = 0;
                if ((len = str.Read(buf, 0, 2048)) <= 0)
                {
                    return 0;
                }
            }
            return buf[ptr++];
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        char Char()
        {
            byte b = 0;
            do b = read();
            while (b < 33 || 126 < b);
            return (char)b;
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        virtual public string Scan()
        {
            var sb = new StringBuilder();
            for (var b = Char(); b >= 33 && b <= 126; b = (char)read())
                sb.Append(b);
            return sb.ToString();
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        virtual public long Long()
        {
            long ret = 0; byte b = 0; var ng = false;
            do b = read();
            while (b != '-' && (b < '0' || '9' < b));
            if (b == '-') { ng = true; b = read(); }
            for (; true; b = read())
            {
                if (b < '0' || '9' < b)
                    return ng ? -ret : ret;
                else ret = (ret << 3) + (ret << 1) + b - '0';
            }
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        virtual public double Double() { return double.Parse(Scan(), CultureInfo.InvariantCulture); }
    }
    class LIB_FastIODebug : LIB_FastIO
    {
        Queue<string> param = new Queue<string>();
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        string NextString() { if (param.Count == 0) foreach (var item in Console.ReadLine().Split(' ')) param.Enqueue(item); return param.Dequeue(); }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public LIB_FastIODebug() { }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public override string Scan() => NextString();
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public override long Long() => long.Parse(NextString());
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public override double Double() => double.Parse(NextString());
    }
}