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 System.Text;
using CompLib.Util;

public class Program
{
    public void Solve()
    {
        var sc = new Scanner();
        int t = sc.NextInt();
        var sb = new StringBuilder();
        for (int i = 0; i < t; i++)
        {
            Q(sc, sb);
        }

        Console.Write(sb);
    }

    void Q(Scanner sc, StringBuilder sb)
    {
        int n = sc.NextInt();
        int[] k = new int[n];
        var l = new long[n];
        var r = new long[n];
        for (int i = 0; i < n; i++)
        {
            k[i] = sc.NextInt() - 1;
            l[i] = sc.NextInt();
            r[i] = sc.NextInt();
        }

        int[] sorted = new int[n];
        for (int i = 0; i < n; i++)
        {
            sorted[i] = i;
        }

        var p = new List<int>();
        var m = new List<int>();
        for (int i = 0; i < n; i++)
        {
            if (l[i] >= r[i]) p.Add(i);
            else m.Add(i);
        }

        p.Sort((x, y) => k[x] == k[y] ? y.CompareTo(x) : k[x].CompareTo(k[y]));
        m.Sort((x, y) => k[x] == k[y] ? x.CompareTo(y) : k[y].CompareTo(k[x]));
        long ans = 0;
        int[] table = new int[n];
        for (int i = 0; i < n; i++)
        {
            table[i] = -1;
        }

        int index = 0;
        for (int i = 0; i < p.Count; i++)
        {
            while (table[index] != -1)
            {
                index++;
            }

            table[index] = p[i];
            ans += index <= k[p[i]] ? l[p[i]] : r[p[i]];
        }

        index = n - 1;

        for (int i = 0; i < m.Count; i++)
        {
            while (table[index] != -1)
            {
                index--;
            }

            table[index] = m[i];
            ans += index <= k[m[i]] ? l[m[i]] : r[m[i]];
        }

        sb.AppendLine(ans.ToString());
    }

    public static void Main(string[] args) => new Program().Solve();
}

// https://bitbucket.org/camypaper/complib
namespace CompLib.Collections
{
    using System;
    using System.Collections.Generic;

    #region PriorityQueue

    /// <summary>
    /// 指定した型のインスタンスを最も価値が低い順に取り出すことが可能な可変サイズのコレクションを表します．
    /// </summary>
    /// <typeparam name="T">優先度付きキュー内の要素の型を指定します．</typeparam>
    /// <remarks>内部的にはバイナリヒープによって実装されています．</remarks>
    public class PriorityQueue<T>
    {
        readonly List<T> heap = new List<T>();
        readonly Comparison<T> cmp;

        /// <summary>
        /// デフォルトの比較子を使用してインスタンスを初期化します．
        /// </summary>
        /// <remarks>この操作は O(1) で実行されます．</remarks>
        public PriorityQueue()
        {
            cmp = Comparer<T>.Default.Compare;
        }

        /// <summary>
        /// デリゲートで表されるような比較関数を使用してインスタンスを初期化します．
        /// </summary>
        /// <param name="comparison"></param>
        /// <remarks>この操作は O(1) で実行されます．</remarks>
        public PriorityQueue(Comparison<T> comparison)
        {
            cmp = comparison;
        }

        /// <summary>
        /// 指定された比較子を使用してインスタンスを初期化します．
        /// </summary>
        /// <param name="comparer"></param>
        /// <remarks>この操作は O(1) で実行されます．</remarks>
        public PriorityQueue(IComparer<T> comparer)
        {
            cmp = comparer.Compare;
        }

        /// <summary>
        /// 優先度付きキューに要素を追加します．
        /// </summary>
        /// <param name="item">優先度付きキューに追加される要素</param>
        /// <remarks>最悪計算量 O(log N) で実行されます．</remarks>
        public void Enqueue(T item)
        {
            var pos = heap.Count;
            heap.Add(item);
            while (pos > 0)
            {
                var par = (pos - 1) / 2;
                if (cmp(heap[par], item) <= 0)
                    break;
                heap[pos] = heap[par];
                pos = par;
            }

            heap[pos] = item;
        }

        /// <summary>
        /// 優先度付きキューから最も価値が低い要素を削除し，返します．
        /// </summary>
        /// <returns>優先度付きキューから削除された要素．</returns>
        /// <remarks>最悪計算量 O(log N) で実行されます．</remarks>
        public T Dequeue()
        {
            var ret = heap[0];
            var pos = 0;
            var x = heap[heap.Count - 1];

            while (pos * 2 + 1 < heap.Count - 1)
            {
                var lch = pos * 2 + 1;
                var rch = pos * 2 + 2;
                if (rch < heap.Count - 1 && cmp(heap[rch], heap[lch]) < 0) lch = rch;
                if (cmp(heap[lch], x) >= 0)
                    break;
                heap[pos] = heap[lch];
                pos = lch;
            }

            heap[pos] = x;
            heap.RemoveAt(heap.Count - 1);
            return ret;
        }

        /// <summary>
        ///  優先度付きキューに含まれる最も価値が低い要素を削除せずに返します．
        /// </summary>
        /// <returns>優先度付きキューに含まれる最も価値が低い要素．</returns>
        /// <remarks>この操作は O(1) で実行されます．</remarks>
        public T Peek()
        {
            return heap[0];
        }

        /// <summary>
        /// 優先度付きキュー内の要素の数を取得します．
        /// </summary>
        /// <returns>優先度付キュー内にある要素の数</returns>
        /// <remarks>最悪計算量 O(1) で実行されます．</remarks>
        public int Count
        {
            get { return heap.Count; }
        }

        /// <summary>
        /// 優先度付きキュー内に要素が存在するかどうかを O(1) で判定します．
        /// </summary>
        /// <returns>優先度付キュー内にある要素が存在するならば true，そうでなければ　false．</returns>
        /// <remarks>この操作は O(1) で実行されます．</remarks>
        public bool Any()
        {
            return heap.Count > 0;
        }

        /// <summary>
        /// 優先度付きキューに含まれる要素を昇順に並べて返します．
        /// </summary>
        /// <remarks>この操作は計算量 O(N log N)で実行されます．</remarks>
        public T[] Items
        {
            get
            {
                var ret = heap.ToArray();
                Array.Sort(ret, cmp);
                return ret;
            }
        }
    }

    #endregion
}

namespace CompLib.Util
{
    using System;
    using System.Linq;

    class Scanner
    {
        private string[] _line;
        private int _index;
        private const char Separator = ' ';

        public Scanner()
        {
            _line = new string[0];
            _index = 0;
        }

        public string Next()
        {
            while (_index >= _line.Length)
            {
                _line = Console.ReadLine().Split(Separator);
                _index = 0;
            }

            return _line[_index++];
        }

        public int NextInt() => int.Parse(Next());
        public long NextLong() => long.Parse(Next());
        public double NextDouble() => double.Parse(Next());
        public decimal NextDecimal() => decimal.Parse(Next());
        public char NextChar() => Next()[0];
        public char[] NextCharArray() => Next().ToCharArray();

        public string[] Array()
        {
            _line = Console.ReadLine().Split(Separator);
            _index = _line.Length;
            return _line;
        }

        public int[] IntArray() => Array().Select(int.Parse).ToArray();
        public long[] LongArray() => Array().Select(long.Parse).ToArray();
        public double[] DoubleArray() => Array().Select(double.Parse).ToArray();
        public decimal[] DecimalArray() => Array().Select(decimal.Parse).ToArray();
    }
}