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: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.IO;
using SB = System.Text.StringBuilder;
//using System.Text.RegularExpressions;
//using System.Globalization;
//using System.Diagnostics;
using static System.Console;
using static System.Math;
using pair = Pair<long, long>;

class Program
{
    static void Main()
    {
        SetOut(new StreamWriter(OpenStandardOutput()) { AutoFlush = false });
        int T = int.Parse(ReadLine());
        for (int i = 0; i < T; i++)
        {
            //Write($"Case #{i + 1}: ");
            new Program().solve();
        }
        Out.Flush();
    }
    readonly Scanner cin = new Scanner();
    readonly int[] dd = { 0, 1, 0, -1, 0 }; //→↓←↑
    readonly int mod = 1000000007;
    readonly int dom = 998244353;
    bool chmax<T>(ref T a, T b) where T : IComparable<T> { if (a.CompareTo(b) < 0) { a = b; return true; } return false; }
    bool chmin<T>(ref T a, T b) where T : IComparable<T> { if (b.CompareTo(a) < 0) { a = b; return true; } return false; }


    void solve()
    {
        int N = cin.nextint;
        var K = new int[N];
        var L = new long[N];
        var R = new long[N];

        var A = new List<pair>();
        var B = new List<pair>();

        long sum = 0;
        for (int i = 0; i < N; i++)
        {
            K[i] = cin.nextint;
            L[i] = cin.nextint;
            R[i] = cin.nextint;

            sum += R[i];
            if (L[i] - R[i] > 0)
            {
                A.Add(new pair(K[i], L[i] - R[i]));
            }
            else if(L[i] - R[i] < 0)
            {
                B.Add(new pair(-K[i], R[i] - L[i]));
            }

        }

        var P = new PriorityQueue<long>(-1);
        A.Sort();


        foreach (var v in A)
        {
            long k = v.f;
            //先頭がk個より少ない
            if (P.Count < k)
            {
                P.Enqueue(v.s);
                sum += v.s;
            }
            else if (P.Count == k)
            {
                if (P.Peek < v.s)
                {
                    var d = P.Dequeue();
                    sum -= d;
                    P.Enqueue(v.s);
                    sum += v.s;
                }

            }
            else
            {
                throw new IndexOutOfRangeException();
            }
        }

        var Q = new PriorityQueue<long>(-1);
        B.Sort();
        foreach (var v in B)
        {
            long k = N + v.f;
            //WriteLine($"k={k}");
            if (k == 0)
            {
                sum -= v.s;
            }
            else if (Q.Count < k)
            {
                Q.Enqueue(v.s);
            }
            else if(Q.Count == k)
            {
                if (Q.Peek < v.s)
                {
                    var d = Q.Dequeue();
                    sum -= d;
                    Q.Enqueue(v.s);

                }
                else
                {
                    sum -= v.s;
                }
            }
            else
            {
                throw new IndexOutOfRangeException();
            }
        }


        WriteLine(sum);
    }

}


class PriorityQueue<T> where T : IComparable<T>
{
    List<T> heap;
    readonly int cmp;
    public PriorityQueue(int cmp = 1) { heap = new List<T>(); this.cmp = cmp; }
    public void Enqueue(T x)
    {
        heap.Add(x);
        int i = Count++;
        while (i > 0)
        {
            int p = (i - 1) >> 1;
            if (x.CompareTo(heap[p]) * cmp <= 0) break;
            heap[i] = heap[p]; i = p;
        }
        heap[i] = x;
    }
    public T Dequeue()
    {
        T ret = heap[0]; T x = heap[--Count];
        int i = 0;
        while ((i << 1) + 1 < Count)
        {
            int a = (i << 1) + 1; int b = (i << 1) + 2;
            if (b < Count && heap[a].CompareTo(heap[b]) * cmp < 0) a = b;
            if (x.CompareTo(heap[a]) * cmp >= 0) break;
            heap[i] = heap[a]; i = a;
        }
        heap[i] = x; heap.RemoveAt(Count);
        return ret;
    }
    public int Count { get; private set; }
    public bool Any => Count > 0;
    public T Peek => heap[0];
}

static class Ex
{
    public static void join<T>(this IEnumerable<T> values, string sep = " ") => WriteLine(string.Join(sep, values));
    public static string concat<T>(this IEnumerable<T> values) => string.Concat(values);
    public static string reverse(this string s) { var t = s.ToCharArray(); Array.Reverse(t); return t.concat(); }

    public static int lower_bound<T>(this IList<T> arr, T val) where T : IComparable<T>
    {
        int low = 0, high = arr.Count;
        int mid;
        while (low < high)
        {
            mid = ((high - low) >> 1) + low;
            if (arr[mid].CompareTo(val) < 0) low = mid + 1;
            else high = mid;
        }
        return low;
    }
    public static int upper_bound<T>(this IList<T> arr, T val) where T : IComparable<T>
    {
        int low = 0, high = arr.Count;
        int mid;
        while (low < high)
        {
            mid = ((high - low) >> 1) + low;
            if (arr[mid].CompareTo(val) <= 0) low = mid + 1;
            else high = mid;
        }
        return low;
    }
}

class Pair<T, U> : IComparable<Pair<T, U>> where T : IComparable<T> where U : IComparable<U>
{
    public T f; public U s;
    public Pair(T f, U s) { this.f = f; this.s = s; }
    public int CompareTo(Pair<T, U> a) => f.CompareTo(a.f) != 0 ? f.CompareTo(a.f) : s.CompareTo(a.s);
    public override string ToString() => $"{f} {s}";
}

class Scanner
{
    string[] s; int i;
    readonly char[] cs = new char[] { ' ' };
    public Scanner() { s = new string[0]; i = 0; }
    public string[] scan => ReadLine().Split();
    public int[] scanint => Array.ConvertAll(scan, int.Parse);
    public long[] scanlong => Array.ConvertAll(scan, long.Parse);
    public double[] scandouble => Array.ConvertAll(scan, double.Parse);
    public string next
    {
        get
        {
            if (i < s.Length) return s[i++];
            string st = ReadLine();
            while (st == "") st = ReadLine();
            s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
            i = 0;
            return next;
        }
    }
    public int nextint => int.Parse(next);
    public long nextlong => long.Parse(next);
    public double nextdouble => double.Parse(next);
}