Problem:
Score : 600 points

Problem Statement

There is a function f(x), which is initially a constant function f(x) = 0.

We will ask you to process Q queries in order. There are two kinds of queries, update queries and evaluation queries, as follows:

An update query 1 a b: Given two integers a and b, let g(x) = f(x) + |x - a| + b and replace f(x) with g(x).

An evaluation query 2: Print x that minimizes f(x), and the minimum value of f(x). If there are multiple such values of x, choose the minimum such value.

We can show that the values to be output in an evaluation query are always integers, so we ask you to print those values as integers without decimal points.

Constraints

All values in input are integers.

1 \leq Q \leq 2 \times 10^5

-10^9 \leq a, b \leq 10^9

The first query is an update query.

Input

Input is given from Standard Input in the following format:

Q
Query_1
:
Query_Q

See Sample Input 1 for an example.

Output

For each evaluation query, print a line containing the response, in the order in which the queries are given.

The response to each evaluation query should be the minimum value of x that minimizes f(x), and the minimum value of f(x), in this order, with space in between.

Sample Input 1

4
1 4 2
2
1 1 -8
2

Sample Output 1

4 2
1 -3

In the first evaluation query, f(x) = |x - 4| + 2, which attains the minimum value of 2 at x = 4.

In the second evaluation query, f(x) = |x - 1| + |x - 4| - 6, which attains the minimum value of -3 when 1 \leq x \leq 4. Among the multiple values of x that minimize f(x), we ask you to print the minimum, that is, 1.

Sample Input 2

4
1 -1000000000 1000000000
1 -1000000000 1000000000
1 -1000000000 1000000000
2

Sample Output 2

-1000000000 3000000000

Solution in C# (Mono 4.6.2.0) (judge verdict: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;
using BitArray = System.Collections.BitArray;
using BigInteger = System.Numerics.BigInteger;

namespace AtCoderProject
{
    public class Program
    {
        public object Calc()
        {
            var Q = consoleReader.Int();
            var result = new List<string>(Q);
            var sorted = new SortedCollection<int>();

            long left = 0;
            long right = 0;
            long bottom = 0;
            foreach (var query in consoleReader.RepeatSplitInt(Q))
            {
                if (query[0] == 1)
                {
                    var item = query[1];
                    bottom += query[2];
                    var insertIndex = sorted.Add(item);
                    var halfIndex = sorted.Count / 2;
                    if (sorted.Count % 2 == 0)
                    {
                        if (insertIndex < halfIndex)
                        {
                            left += item;
                            right += sorted[halfIndex];
                        }
                        else
                        {
                            left += sorted[halfIndex - 1];
                            right += item;
                        }
                    }
                    else
                    {
                        if (insertIndex < halfIndex)
                        {
                            left += item - sorted[halfIndex];
                        }
                        else if (insertIndex > halfIndex)
                        {
                            right += item - sorted[halfIndex];
                        }
                    }
                }
                else
                {
                    long sum = bottom + right - left;
                    result.Add($"{sorted[(sorted.Count - 1) / 2]} {sum}");
                }
            }

            return MultiLine(result);
        }

        class SortedCollection<T> : List<T>
        {
            private IComparer<T> Comparer { get; }
            public SortedCollection() : this(Comparer<T>.Default) { }
            public SortedCollection(IComparer<T> comparer) { this.Comparer = comparer; }
            public new int Add(T item)
            {
                base.Add(item);
                for (int i = this.Count - 2; i >= 0; i--)
                {
                    var current = this[i];
                    if (Comparer.Compare(item, current) < 0)
                        this[i + 1] = current;
                    else
                    {
                        this[i + 1] = item;
                        return i + 1;
                    }
                }
                this[0] = item;
                return 0;
            }
        }

        public const int mod = 1000000007;
        #region いつもの
        private readonly ConsoleReader consoleReader;
        public Program() : this(new ConsoleReader()) { }
        public Program(ConsoleReader consoleReader) { this.consoleReader = consoleReader; }
        static void Main() => Console.WriteLine(new Program().Calc()); static string MultiLine<T>(IEnumerable<T> source) => string.Join("\n", source);
        #endregion
    }

    #region Console
    public class ConsoleReader { public virtual string String() => Console.ReadLine(); public int Int() => int.Parse(String()); public long Long() => long.Parse(String()); public ulong ULong() => ulong.Parse(String()); public double Double() => double.Parse(String()); public string[] Split() => String().Split().ToArray(); public int[] SplitInt() => String().Split().Select(int.Parse).ToArray(); public long[] SplitLong() => String().Split().Select(long.Parse).ToArray(); public ulong[] SplitULong() => String().Split().Select(ulong.Parse).ToArray(); public double[] SplitDouble() => String().Split().Select(double.Parse).ToArray(); public IEnumerable<string> Repeat(int count) { for (int i = 0; i < count; i++) yield return String(); } public IEnumerable<int> RepeatInt(int count) { for (int i = 0; i < count; i++) yield return Int(); } public IEnumerable<long> RepeatLong(int count) { for (int i = 0; i < count; i++) yield return Long(); } public IEnumerable<string[]> RepeatSplit(int count) { for (int i = 0; i < count; i++) yield return Split(); } public IEnumerable<int[]> RepeatSplitInt(int count) { for (int i = 0; i < count; i++) yield return SplitInt(); } }
    #endregion
}