Problem:
Score : 600 points

Problem Statement

We have N points numbered 1 to N arranged in a line in this order.

Takahashi decides to make an undirected graph, using these points as the vertices.
In the beginning, the graph has no edge. Takahashi will do M operations to add edges in this graph.
The i-th operation is as follows:

The operation uses integers L_i and R_i between 1 and N (inclusive), and a positive integer C_i. For every pair of integers (s, t) such that L_i \leq s < t \leq R_i, add an edge of length C_i between Vertex s and Vertex t.

The integers L_1, ..., L_M, R_1, ..., R_M, C_1, ..., C_M are all given as input.

Takahashi wants to solve the shortest path problem in the final graph obtained. Find the length of the shortest path from Vertex 1 to Vertex N in the final graph.

Constraints

2 \leq N \leq 10^5

1 \leq M \leq 10^5

1 \leq L_i < R_i \leq N

1 \leq C_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N M
L_1 R_1 C_1
:
L_M R_M C_M

Output

Print the length of the shortest path from Vertex 1 to Vertex N in the final graph.
If there is no shortest path, print -1 instead.

Sample Input 1

4 3
1 3 2
2 4 3
1 4 6

Sample Output 1

5

We have an edge of length 2 between Vertex 1 and Vertex 2, and an edge of length 3 between Vertex 2 and Vertex 4, so there is a path of length 5 between Vertex 1 and Vertex 4.

Sample Input 2

4 2
1 2 1
3 4 2

Sample Output 2

-1

Sample Input 3

10 7
1 5 18
3 4 8
1 3 5
4 7 10
5 9 8
6 10 5
8 10 3

Sample Output 3

28

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

using System;
using System.Collections;
using System.Collections.Generic;
using System.Globalization;
using System.IO;
using System.Linq;
using System.Numerics;
using E = System.Linq.Enumerable;

internal partial class Solver {
    public void Run() {
        var N = ni();
        var M = ni();
        var L = new int[M];
        var R = new int[M];
        var C = new int[M];
        for (int i = 0; i < M; i++) {
            L[i] = ni() - 1;
            R[i] = ni() - 1;
            C[i] = ni();
        }


        var dp = new long[N];
        const long inf = long.MaxValue;
        for (int i = 1; i < N; i++) dp[i] = inf;

        var addEvents = E.Range(0, N + 1).Select(_ => new List<long>()).ToArray();
        var removeEvents = E.Range(0, N + 1).Select(_ => new List<long>()).ToArray();

        for (int i = 0; i < M; i++) {
            addEvents[L[i]].Add(i);
        }
        var set = new MultiSet<long>();
        for (int i = 0; i < N; i++) {
            foreach (var val in removeEvents[i]) {
                set.Remove(val);
            }
            if (set.Count > 0) {
                dp[i] = Math.Min(dp[i], set.At(0));
            }
            if (dp[i] == inf) break;
            foreach (var id in addEvents[i]) {
                set.Add(dp[i] + C[id]);
                removeEvents[R[id] + 1].Add(dp[i] + C[id]);
            }
        }
        long ans = dp[N - 1];
        if (ans == inf) ans = -1;
        cout.WriteLine(ans);
    }
}


public partial class MultiSet<T> {
    private readonly LLRBTreeNode<T> end = new LLRBTreeNode<T>(default(T));
    private LLRBTreeNode<T> root = null;
    private readonly IComparer<T> _comparer;


    public MultiSet() : this(Comparer<T>.Default) {
    }

    public MultiSet(IComparer<T> comparer) {
        _comparer = comparer;
        root = end;
    }

    protected virtual bool AllowMultiple { get { return true; } }

    public int Count { get { return root == null ? 0 : root.Count + root.LeftTotalCount + root.RightTotalCount - 1; } }

    private LLRBTreeNode<T> FindNode(T value) {
        var node = root;
        while (node != null) {
            int cmp = Compare(value, node);
            if (cmp == 0) {
                return node;
            }
            node = (cmp < 0) ? node.Left : node.Right;
        }
        return null;
    }

    public void Clear() {
        root = end;
    }

    public bool Contains(T value) {
        var node = FindNode(value);
        return node != null;
    }

    public int CountOf(T value) {
        var node = FindNode(value);
        return node != null ? node.Count : 0;
    }

    public int IndexOfLowerBound(T value) {
        var node = root;
        int index = 0;
        while (node != null) {
            int cmp = Compare(value, node);
            if (cmp <= 0) {
                node = node.Left;
            } else {
                index += node.LeftTotalCount + node.Count;
                node = node.Right;
            }
        }
        return index;
    }

    private int Compare(T value, LLRBTreeNode<T> node) {
        if (node == end) {
            return -1;
        }

        return _comparer.Compare(value, node.Value);
    }

    public int IndexOfUpperBound(T value) {
        var node = root;
        int index = 0;
        while (node != null) {
            int cmp = Compare(value, node);
            if (cmp < 0) {
                node = node.Left;
            } else {
                index += node.LeftTotalCount + node.Count;
                node = node.Right;
            }
        }
        return index;
    }

    public T At(int index) {
        var node = root;
        while (node != null) {
            int leftCount = node.LeftTotalCount;
            if (leftCount <= index && index < leftCount + node.Count) {
                return node.Value;
            }

            if (index < leftCount) {
                node = node.Left;
            } else {
                index -= leftCount + node.Count;
                node = node.Right;
            }
        }
        throw new ArgumentOutOfRangeException("index");
    }

    public LLRBTreeIterator<T> AtIterator(int index) {
        var node = root;
        while (node != null) {
            int leftCount = node.LeftTotalCount;
            if (leftCount <= index && index < leftCount + node.Count) {
                return new LLRBTreeIterator<T>(node, index - leftCount);
            }

            if (index < leftCount) {
                node = node.Left;
            } else {
                index -= leftCount + node.Count;
                node = node.Right;
            }
        }
        throw new ArgumentOutOfRangeException("index");
    }

    public void Add(T value) {
        root = Add(root, value);
        root.Color = LLRBTreeNode<T>.BLACK;
    }

    private LLRBTreeNode<T> Add(LLRBTreeNode<T> h, T value) {
        if (h == null) {
            return new LLRBTreeNode<T>(value);
        }

        int cmp = Compare(value, h);
        if (cmp == 0) {
            if (AllowMultiple) {
                h.Count++;
                FixCount(h);
            }
        } else if (cmp <= 0) {
            h.Left = Add(h.Left, value);
            FixCount(h);
        } else {
            h.Right = Add(h.Right, value);
            FixCount(h);
        }

        if (IsRed(h.Right) && !IsRed(h.Left)) {
            h = RotateLeft(h);
        }

        if (IsRed(h.Left) && IsRed(h.Left.Left)) {
            h = RotateRight(h);
        }

        if (IsRed(h.Left) && IsRed(h.Right)) {
            ColorFlip(h);
        }

        return h;
    }

    private LLRBTreeNode<T> RemoveLeftestNode(LLRBTreeNode<T> h, out LLRBTreeNode<T> leftMost) {
        if (h.Left == null) {
            leftMost = h;
            return null;
        }

        if (!IsRed(h.Left) && !IsRed(h.Left.Left)) {
            h = MoveRedLeft(h);
        }

        h.Left = RemoveLeftestNode(h.Left, out leftMost);
        return FixUp(h);
    }

    private bool TryReduceCount(LLRBTreeNode<T> h, T value, out int num) {
        num = 0;
        if (h == null) {
            return false;
        }

        int cmp = Compare(value, h);
        if (cmp == 0) {
            num = h.Count;
            if (h.Count > 1) {
                h.Count--;
                FixCount(h);
                return true;
            }
            return false;
        }
        if (TryReduceCount((cmp < 0) ? h.Left : h.Right, value, out num)) {
            FixCount(h);
            return true;
        }
        return false;
    }


    public bool Remove(T value) {
        if (AllowMultiple) {
            int num;
            if (TryReduceCount(root, value, out num)) {
                return true;
            }
            if (num == 0) {
                return false;
            }
        } else {
            if (!Contains(value)) {
                return false;
            }
        }

        root = RemoveNode(root, value);
        if (root != null) {
            root.Color = LLRBTreeNode<T>.BLACK;
        }
        return true;
    }

    private LLRBTreeNode<T> RemoveNode(LLRBTreeNode<T> h, T value) {
        if (Compare(value, h) < 0) {
            if (h.Left == null) {
                throw new KeyNotFoundException("value");
            }

            if (!IsRed(h.Left) && !IsRed(h.Left.Left)) {
                h = MoveRedLeft(h);
            }
            h.Left = RemoveNode(h.Left, value);
            FixCount(h);
        } else {
            if (IsRed(h.Left)) {
                h = RotateRight(h);
            }

            if (h.Right == null) {
                if (Compare(value, h) == 0) {
                    return null;
                }

                throw new KeyNotFoundException("value");
            }

            if (!IsRed(h.Right) && !IsRed(h.Right.Left)) {
                h = MoveRedRight(h);
            }

            if (Compare(value, h) == 0) {
                LLRBTreeNode<T> sub;
                h.Right = RemoveLeftestNode(h.Right, out sub);
                h = Substitute(h, sub);
                FixCount(h);
            } else {
                h.Right = RemoveNode(h.Right, value);
                FixCount(h);
            }
        }

        return FixUp(h);
    }

    private LLRBTreeNode<T> Substitute(LLRBTreeNode<T> node, LLRBTreeNode<T> sub) {
        sub.Parent = node.Parent;
        sub.Left = node.Left;
        sub.Right = node.Right;
        sub.TotalCount = node.TotalCount;
        sub.Color = node.Color;

        if (sub.Parent != null) {
            if (sub.Parent.Left == node) {
                sub.Parent.Left = sub;
            }

            if (sub.Parent.Right == node) {
                sub.Parent.Right = sub;
            }
        }
        if (sub.Left != null) {
            sub.Left.Parent = sub;
        }

        if (sub.Right != null) {
            sub.Right.Parent = sub;
        }

        return sub;
    }

    private static LLRBTreeNode<T> MoveRedLeft(LLRBTreeNode<T> h) {
        ColorFlip(h);

        if (IsRed(h.Right.Left)) {
            h.Right = RotateRight(h.Right);
            FixCount(h);
            h = RotateLeft(h);
            ColorFlip(h);
        }

        return h;
    }

    private static LLRBTreeNode<T> MoveRedRight(LLRBTreeNode<T> h) {
        ColorFlip(h);

        if (IsRed(h.Left.Left)) {
            h = RotateRight(h);
            ColorFlip(h);
        }

        return h;
    }

    private static LLRBTreeNode<T> RotateLeft(LLRBTreeNode<T> h) {
        var x = h.Right;
        h.Right = x.Left;
        x.Left = h;

        x.Color = h.Color;
        h.Color = LLRBTreeNode<T>.RED;
        FixCount(h);
        FixCount(x);
        return x;
    }

    private static LLRBTreeNode<T> RotateRight(LLRBTreeNode<T> h) {
        var x = h.Left;
        h.Left = x.Right;
        x.Right = h;

        x.Color = h.Color;
        h.Color = LLRBTreeNode<T>.RED;
        FixCount(h);
        FixCount(x);
        return x;
    }

    private static bool IsRed(LLRBTreeNode<T> h) {
        return h != null && h.Color == LLRBTreeNode<T>.RED;
    }

    private static void ColorFlip(LLRBTreeNode<T> h) {
        h.Color = !h.Color;
        h.Left.Color = !h.Left.Color;
        h.Right.Color = !h.Right.Color;
    }

    private static LLRBTreeNode<T> GetLeftestNode(LLRBTreeNode<T> h) {
        while (h.Left != null) {
            h = h.Left;
        }
        return h;
    }

    private static LLRBTreeNode<T> FixUp(LLRBTreeNode<T> h) {
        if (IsRed(h.Right)) {
            h = RotateLeft(h);
        }

        if (h.Left != null && IsRed(h.Left) && IsRed(h.Left.Left)) {
            h = RotateRight(h);
        }

        if (IsRed(h.Left) && IsRed(h.Right)) {
            ColorFlip(h);
        }
        FixCount(h);
        return h;
    }

    private static void FixCount(LLRBTreeNode<T> node) {
        node.TotalCount = node.Count + node.LeftTotalCount + node.RightTotalCount;
    }

    public void Debug() {
        if (root != null) {
            root.Debug();
        }
    }
}

public class LLRBTreeNode<T> {
    public const bool RED = true;
    public const bool BLACK = false;
    public T Value;
    public bool Color = RED;
    public LLRBTreeNode<T> Parent { get; set; }
    private LLRBTreeNode<T> _left;
    private LLRBTreeNode<T> _right;
    public LLRBTreeNode<T> Left {
        get { return _left; }
        set {
            if (_left == value) {
                return;
            }

            if (_left != null && _left.Parent == this) {
                _left.Parent = null;
            }

            _left = value;
            if (_left != null) {
                _left.Parent = this;
            }
        }
    }
    public LLRBTreeNode<T> Right {
        get { return _right; }
        set {
            if (_right == value) {
                return;
            }

            if (_right != null && _right.Parent == this) {
                _right.Parent = null;
            }

            _right = value;
            if (_right != null) {
                _right.Parent = this;
            }
        }
    }
    public int Count = 1;
    public LLRBTreeNode(T value) {
        Value = value;
    }

    public int TotalCount = 1;
    public int LeftTotalCount { get { return Left == null ? 0 : Left.TotalCount; } }
    public int RightTotalCount { get { return Right == null ? 0 : Right.TotalCount; } }

    public void Debug(string indent = "") {
        Console.WriteLine(indent + ":" + Value + " - " + Count + " - " + TotalCount);
        if (Left != null) {
            Left.Debug(indent + "L");
        }
        if (Right != null) {
            Right.Debug(indent + "R");
        }
    }
}

public struct LLRBTreeIterator<T> {
    private readonly LLRBTreeNode<T> _node;
    private readonly int _index;

    public LLRBTreeIterator(LLRBTreeNode<T> node, int index = 0) {
        _node = node;
        _index = index;
    }

    public T Value { get { return _node.Value; } }

    public static LLRBTreeIterator<T> operator ++(LLRBTreeIterator<T> x) {
        return x.GetSuccessor();
    }

    public static LLRBTreeIterator<T> operator --(LLRBTreeIterator<T> x) {
        return x.GetPredecessor();
    }

    private LLRBTreeIterator<T> GetSuccessor() {
        if (_index + 1 < _node.Count) {
            return new LLRBTreeIterator<T>(_node, _index + 1);
        } else {
            LLRBTreeNode<T> current, parent;
            if (_node.Right == null) {
                for (current = _node, parent = _node.Parent; parent.Right == current; current = parent, parent = current.Parent) {
                    ;
                }

                return new LLRBTreeIterator<T>(parent);
            } else {
                for (parent = _node.Right, current = parent.Left; current != null; parent = current, current = parent.Left) {
                    ;
                }

                return new LLRBTreeIterator<T>(parent);
            }
        }
    }

    private LLRBTreeIterator<T> GetPredecessor() {
        if (0 <= _index - 1) {
            return new LLRBTreeIterator<T>(_node, _index - 1);
        } else {
            LLRBTreeNode<T> current, parent;
            if (_node.Left == null) {
                for (current = _node, parent = _node.Parent; parent.Left == current; current = parent, parent = current.Parent) {
                    ;
                }

                return new LLRBTreeIterator<T>(parent, parent.Count - 1);
            } else {
                for (parent = _node.Left, current = parent.Right; current != null; parent = current, current = parent.Right) {
                    ;
                }

                return new LLRBTreeIterator<T>(parent, parent.Count - 1);
            }
        }
    }
}

public partial class MultiSet<T> : IEnumerable<T> {
    public IEnumerator<T> GetEnumerator() {
        var node = root;
        var stack = new Stack<LLRBTreeNode<T>>();
        while (node != null || stack.Count > 0) {
            while (node != null) {
                stack.Push(node);
                node = node.Left;
            }
            node = stack.Pop();
            if (node == end) {
                break;
            }

            int count = node.Count;
            for (int i = 0; i < count; i++) {
                yield return node.Value;
            }
            node = node.Right;
        }
    }

    IEnumerator IEnumerable.GetEnumerator() {
        return GetEnumerator();
    }
}
// PREWRITEN CODE BEGINS FROM HERE
internal partial class Solver : Scanner {
    public static void Main(string[] args) {
#if LOCAL
        byte[] inputBuffer = new byte[1000000];
        var inputStream = Console.OpenStandardInput(inputBuffer.Length);
        Console.SetIn(new StreamReader(inputStream, Console.InputEncoding, false, inputBuffer.Length));
        new Solver(Console.In, Console.Out).Run();
#else
        Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false });
        new Solver(Console.In, Console.Out).Run();
        Console.Out.Flush();
#endif
    }

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

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

internal static class LinqPadExtension {
    public static T Dump<T>(this T obj) {
#if LOCAL
        return LINQPad.Extensions.Dump(obj);
#else
        return obj;
#endif
    }
}

public class Scanner {
    private readonly TextReader Reader;
    private readonly Queue<string> TokenQueue = new Queue<string>();
    private readonly CultureInfo ci = CultureInfo.InvariantCulture;

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

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

    public int NextInt() { return int.Parse(Next(), ci); }
    public long NextLong() { return long.Parse(Next(), ci); }
    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 (TokenQueue.Count == 0) {
            if (!StockTokens()) {
                throw new InvalidOperationException();
            }
        }
        return TokenQueue.Dequeue();
    }

    public bool HasNext() {
        if (TokenQueue.Count > 0) {
            return true;
        }

        return StockTokens();
    }

    private static readonly char[] _separator = new[] { ' ', '\t' };
    private bool StockTokens() {
        while (true) {
            string line = Reader.ReadLine();
            if (line == null) {
                return false;
            }

            string[] tokens = line.Split(_separator, StringSplitOptions.RemoveEmptyEntries);
            if (tokens.Length == 0) {
                continue;
            }

            foreach (string token in tokens) {
                TokenQueue.Enqueue(token);
            }

            return true;
        }
    }
}