Problem:
Score : 500 points

Problem Statement

We have N camels numbered 1,2,\ldots,N.
Snuke has decided to make them line up in a row.

The happiness of Camel i will be L_i if it is among the K_i frontmost camels, and R_i otherwise.

Snuke wants to maximize the total happiness of the camels. Find the maximum possible total happiness of the camel.

Solve this problem for each of the T test cases given.

Constraints

All values in input are integers.

1 \leq T \leq 10^5

1 \leq N \leq 2 \times 10^{5}

1 \leq K_i \leq N

1 \leq L_i, R_i \leq 10^9

The sum of values of N in each input file is at most 2 \times 10^5.

Input

Input is given from Standard Input in the following format:

T
\mathrm{case}_1
\vdots
\mathrm{case}_T

Each case is given in the following format:

N
K_1 L_1 R_1
\vdots
K_N L_N R_N

Output

Print T lines. The i-th line should contain the answer to the i-th test case.

Sample Input 1

3
2
1 5 10
2 15 5
3
2 93 78
1 71 59
3 57 96
19
19 23 16
5 90 13
12 85 70
19 67 78
12 16 60
18 48 28
5 4 24
12 97 97
4 57 87
19 91 74
18 100 76
7 86 46
9 100 57
3 76 73
6 84 93
1 6 84
11 75 94
19 15 3
12 11 34

Sample Output 1

25
221
1354

In the first test case, it is optimal to line up the camels in the order 2, 1.

Camel 1 is not the frontmost camel, so its happiness will be 10.

Camel 2 is among the two frontmost camels, so its happiness will be 15.

In the second test case, it is optimal to line up the camels in the order 2, 1, 3.

Camel 1 is among the two frontmost camels, so its happiness will be 93.

Camel 2 is the frontmost camel, so its happiness will be 71.

Camel 3 is among the three frontmost camels, so its happiness will be 57.

Solution in C# (.NET Core 3.1.201) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using static Assistant.Input;
using static Assistant.Debug;
using System.Linq;
using Assistant;
using System.Text;

namespace エイシングプログラミングコンテスト2020E_2
{
    class Program
    {
        static void Main(string[] args)
        {
            var T = RInt;

            StringBuilder sb = new StringBuilder();
            for (int t = 0; t < T; t++)
            {
                N = RInt;
                Rakda[] rakdas = new Rakda[N];
                for (int i = 0; i < N; i++)
                {
                    int k = RInt - 1;
                    int l1 = RInt;
                    int r1 = RInt;
                    rakdas[i] = new Rakda { K = k, L = l1, R = r1 };
                }

                var rakdas1 = rakdas.Where(x => x.S >= 0).OrderByDescending(x => x.S).ToArray();
                var rakdas2 = rakdas.Where(x => x.S < 0).OrderBy(x => x.S).ToArray();

                long ans = 0;
                ans += Get(rakdas1, true);
                ans += Get(rakdas2, false);

                sb.AppendLine(ans.ToString());

                Draw1D(rakdas1.Select(x => x.S).ToArray());
                Draw1D(rakdas2.Select(x => x.S).ToArray());
            }

            Console.Write(sb);
        }

        static int N;
        static long Get(Rakda[] rakdas, bool plus)
        {
            int max = -1;
            int[] use = new int[rakdas.Length];
            Set<int> rem = new Set<int>();

            long ret = 0;
            int length = rakdas.Length;
            foreach (var rak in rakdas)
            {
                int k = rak.K;
                if (!plus) k = N - 2 - k;

                if (k > max)
                {
                    for (int i = max + 1; i <= k && i < length; i++)
                    {
                        if (use[i] == 1) continue;
                        rem.Add(i);
                    }
                    max = k;
                }

                int index = rem.UpperBound(k) - 1;
                if (index < 0)
                {
                    if (plus) ret += rak.R;
                    else ret += rak.L;
                    use[length - 1] = 1;
                    length--;
                }
                else
                {
                    use[index] = 1;
                    if (plus) ret += rak.L;
                    else ret += rak.R;
                    rem.Remove(index);
                }
            }

            return ret;
        }

        struct Rakda
        {
            public int K;
            public long L;
            public long R;
            public long S => L - R;
        }
    }

    /// <summary>
    /// Set/MultiSet
    /// </summary>
    /// <typeparam name="T"></typeparam>
    public class Set<T>
    {
        Node root;
        readonly IComparer<T> comparer;
        readonly Node nil;
        public bool IsMultiSet { get; set; }
        public Set(IComparer<T> comparer)
        {
            nil = new Node(default(T));
            root = nil;
            this.comparer = comparer;
        }
        public Set(Comparison<T> comparison) : this(Comparer<T>.Create(comparison)) { }
        public Set() : this(Comparer<T>.Default) { }
        public Set(bool isMultiSet) : this(Comparer<T>.Default) { IsMultiSet = isMultiSet; }
        public bool Add(T v)
        {
            return insert(ref root, v);
        }
        public bool Remove(T v)
        {
            return remove(ref root, v);
        }
        public T this[int index] { get { return find(root, index); } }
        public T Min { get { return this[0]; } }
        public T Max { get { return this[Count - 1]; } }
        public int Count { get { return root.Count; } }
        public void RemoveAt(int k)
        {
            if (k < 0 || k >= root.Count) throw new ArgumentOutOfRangeException();
            removeAt(ref root, k);
        }
        public T[] Items
        {
            get
            {
                var ret = new T[root.Count];
                var k = 0;
                walk(root, ret, ref k);
                return ret;
            }
        }
        void walk(Node t, T[] a, ref int k)
        {
            if (t.Count == 0) return;
            walk(t.lst, a, ref k);
            a[k++] = t.Key;
            walk(t.rst, a, ref k);
        }

        bool insert(ref Node t, T key)
        {
            if (t.Count == 0) { t = new Node(key); t.lst = t.rst = nil; t.Update(); return true; }
            var cmp = comparer.Compare(t.Key, key);
            bool res;
            if (cmp > 0)
                res = insert(ref t.lst, key);
            else if (cmp == 0)
            {
                if (IsMultiSet) res = insert(ref t.lst, key);
                else return false;
            }
            else res = insert(ref t.rst, key);
            balance(ref t);
            return res;
        }
        bool remove(ref Node t, T key)
        {
            if (t.Count == 0) return false;
            var cmp = comparer.Compare(key, t.Key);
            bool ret;
            if (cmp < 0) ret = remove(ref t.lst, key);
            else if (cmp > 0) ret = remove(ref t.rst, key);
            else
            {
                ret = true;
                var k = t.lst.Count;
                if (k == 0) { t = t.rst; return true; }
                if (t.rst.Count == 0) { t = t.lst; return true; }


                t.Key = find(t.lst, k - 1);
                removeAt(ref t.lst, k - 1);
            }
            balance(ref t);
            return ret;
        }
        void removeAt(ref Node t, int k)
        {
            var cnt = t.lst.Count;
            if (cnt < k) removeAt(ref t.rst, k - cnt - 1);
            else if (cnt > k) removeAt(ref t.lst, k);
            else
            {
                if (cnt == 0) { t = t.rst; return; }
                if (t.rst.Count == 0) { t = t.lst; return; }

                t.Key = find(t.lst, k - 1);
                removeAt(ref t.lst, k - 1);
            }
            balance(ref t);
        }
        void balance(ref Node t)
        {
            var balance = t.lst.Height - t.rst.Height;
            if (balance == -2)
            {
                if (t.rst.lst.Height - t.rst.rst.Height > 0) { rotR(ref t.rst); }
                rotL(ref t);
            }
            else if (balance == 2)
            {
                if (t.lst.lst.Height - t.lst.rst.Height < 0) rotL(ref t.lst);
                rotR(ref t);
            }
            else t.Update();
        }

        T find(Node t, int k)
        {
            if (k < 0 || k > root.Count) throw new ArgumentOutOfRangeException();
            for (; ; )
            {
                if (k == t.lst.Count) return t.Key;
                else if (k < t.lst.Count) t = t.lst;
                else { k -= t.lst.Count + 1; t = t.rst; }
            }
        }
        public int LowerBound(T v)
        {
            var k = 0;
            var t = root;
            for (; ; )
            {
                if (t.Count == 0) return k;
                if (comparer.Compare(v, t.Key) <= 0) t = t.lst;
                else { k += t.lst.Count + 1; t = t.rst; }
            }
        }
        public int UpperBound(T v)
        {
            var k = 0;
            var t = root;
            for (; ; )
            {
                if (t.Count == 0) return k;
                if (comparer.Compare(t.Key, v) <= 0) { k += t.lst.Count + 1; t = t.rst; }
                else t = t.lst;
            }
        }

        void rotR(ref Node t)
        {
            var l = t.lst;
            t.lst = l.rst;
            l.rst = t;
            t.Update();
            l.Update();
            t = l;
        }
        void rotL(ref Node t)
        {
            var r = t.rst;
            t.rst = r.lst;
            r.lst = t;
            t.Update();
            r.Update();
            t = r;
        }


        class Node
        {
            public Node(T key)
            {
                Key = key;
            }
            public int Count { get; private set; }
            public sbyte Height { get; private set; }
            public T Key { get; set; }
            public Node lst, rst;
            public void Update()
            {
                Count = 1 + lst.Count + rst.Count;
                Height = (sbyte)(1 + Math.Max(lst.Height, rst.Height));
            }
            public override string ToString()
            {
                return string.Format("Count = {0}, Key = {1}", Count, Key);
            }
        }
    }

}

namespace Assistant
{
    static class Input
    {
        static List<string> line = new List<string>();
        static int index = 0;
        static String RNext()
        {
            if (line.Count <= index) line.AddRange(Console.ReadLine().Split());
            return line[index++];
        }
        public static int RInt => int.Parse(RNext());
        public static long RLong => long.Parse(RNext());
        public static int[] RInts => Console.ReadLine().Split().Select(int.Parse).ToArray();
        public static long[] RLongs => Console.ReadLine().Split().Select(long.Parse).ToArray();
        public static string RString => RNext();
        //以下未テスト
        public static int[] RIntsC(int c) => Enumerable.Repeat(0, c).Select(x => int.Parse(RNext())).ToArray();
        public static long[] RLongsC(int c) => Enumerable.Repeat(0, c).Select(x => long.Parse(RNext())).ToArray();
        public static char[][] RMap(int h) => Enumerable.Repeat(0, h).Select(x => Console.ReadLine().ToCharArray()).ToArray();
    }

    public struct Mlong
    {
        long _v;
        const long mod = 1000000007;
        public Mlong(long n = 0) : this() { _v = n >= mod ? n % mod : n; }

        public static implicit operator Mlong(long _x) => new Mlong(_x);
        public static implicit operator long(Mlong _x) => _x._v;
        public static Mlong operator +(Mlong m1, Mlong m2) { long m = m1._v + m2._v; return m >= mod ? m - mod : m; }
        public static Mlong operator -(Mlong m1, Mlong m2) { long m = m1._v - m2._v; return m >= 0 ? m : m + mod; }
        public static Mlong operator *(Mlong m1, Mlong m2) => m1._v * m2._v % mod;
        public static Mlong operator /(Mlong m1, Mlong m2) => m1._v * ModPow(m2._v, mod - 2) % mod;

        public static long ModPow(long a, long n)
        {
            if (n == 0) return 1;
            else if (n % 2 == 1) return a * ModPow(a, n - 1) % mod;
            else return ModPow(a * a % mod, n / 2);
        }

        static Mlong[] fac, finv, inv;
        public static void nCkInit(int max)
        {
            fac = new Mlong[max]; finv = new Mlong[max]; inv = new Mlong[max];
            fac[0] = fac[1] = 1;
            finv[0] = finv[1] = 1;
            inv[1] = 1;
            for (int i = 2; i < max; i++)
            {
                fac[i] = fac[i - 1] * i;
                inv[i] = mod - inv[mod % i] * (mod / i);
                finv[i] = finv[i - 1] * inv[i];
            }
        }

        public static Mlong nCk(int n, int k)
        {
            if (n < k) return 0;
            if (n < 0 || k < 0) return 0;
            return fac[n] * finv[k] * finv[n - k];
        }
    }

    static class Debug
    {
        static public void Draw2D<T>(T[,] map, int mode = 1)
        {
#if DEBUG
            int W = map.GetLength(0);
            int H = map.GetLength(1);

            string[,] map2 = new string[W + 1, H + 1];
            for (int i = 0; i < W + 1; i++)
            {
                for (int j = 0; j < H + 1; j++)
                {
                    if (i == 0 && j == 0) map2[i, j] = 0.ToString();
                    else if (i == 0) map2[i, j] = (j - 1).ToString();
                    else if (j == 0) map2[i, j] = (i - 1).ToString();
                    else map2[i, j] = map[i - 1, j - 1].ToString();
                }
            }

            for (int i = 0; i < W + 1; i++)
            {
                for (int j = 0; j < H + 1; j++)
                {
                    if (mode == 0) Console.Write(map2[i, j].Last());
                    if (mode == 1) Console.Write(map2[i, j] + " ");
                }
                Console.WriteLine();
            }
            Console.WriteLine();
#endif
        }

        public static void Draw1D<T>(T[] array, int mode = 0)
        {
#if DEBUG
            Console.WriteLine(string.Join(" ", array));
#endif
        }
    }
}