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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using static Input;

public class Prog
{
    private const int INF = 1000000007;
    private struct Pair { public int x, y; public Pair(int x, int y) { this.x = x; this.y = y; } }
    public static void Solve()
    {

        int N = NextInt();
        List<long[]> ans = new List<long[]>();
        long b_sum = 0;
        long small_sum = 0;
        long big_sum = 0;
        PriorityQueue<long, long> big = new PriorityQueue<long, long>();
        PriorityQueue<long, long> small = new PriorityQueue<long, long>(false);
        for (int i = 0; i < N; i++)
        {
            int Q = NextInt();
            if (Q == 1)
            {
                int a = NextInt();
                b_sum += NextInt();
                //とりあえずどっちにも追加する
                big.Add(a, a);
                small.Add(a, a);
                big_sum += a;
                small_sum += a;
                //small.top > big.top swap
                if (small.Peek() > big.Peek())
                {
                    var c0 = small.Take();
                    small_sum -= c0;
                    var c1 = big.Take();
                    big_sum -= c1;
                    big.Add(c0, c0);
                    small.Add(c1, c1);
                    big_sum += c0;
                    small_sum += c1;
                }
            }
            else
            {
                //small.top が中央値
                long mid = small.Peek();
                long c_min = mid * (small.Count() / 2) - (small_sum / 2);
                long c_max = (big_sum / 2) - mid * (big.Count() / 2);
                ans.Add(new long[2] { mid, c_max + c_min + b_sum });
            }
        }
        ans.ForEach(v => Console.WriteLine(v[0] + " " + v[1]));
    }

    public static void Main()
    {
        var sw = new System.IO.StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
        Console.SetOut(sw);
        Solve();
        Console.Out.Flush();
    }
}

public class PriorityQueue<Tkey, Tvalue> where Tkey : IComparable
{
    private List<Tkey> keys = new List<Tkey>();
    private List<Tvalue> values = new List<Tvalue>();
    private int size = 0;
    private bool Descending;
    private int Compare(Tkey a, Tkey b) { return (Descending ? a.CompareTo(b) : b.CompareTo(a)); }

    public PriorityQueue(bool b = true) { Clear(); Descending = b; }
    public int Count() { return size; }
    public void Clear() { keys = new List<Tkey>(); values = new List<Tvalue>(); size = 0; }
    public void Add(Tkey e, Tvalue v)
    {
        keys.Add(e);
        values.Add(v);
        int x = size;
        size += 1;
        while (x != 0)
        {
            int par = (x % 2 == 0 ? x - 2 : x - 1) / 2;
            if (Compare(keys[par], e) <= 0) break;
            Tkey a = keys[x]; keys[x] = keys[par]; keys[par] = a;
            Tvalue b = values[x]; values[x] = values[par]; values[par] = b;
            x = par;
        }
    }
    public void Poll()
    {
        Tkey k = keys[size - 1];
        Tvalue v = values[size - 1];
        int x = 0;
        size--;
        if (size == 0) { Clear(); return; }
        keys.RemoveAt(size);
        values.RemoveAt(size);
        while (true)
        {
            int l = x * 2 + 1;
            int r = x * 2 + 2;
            if (size - 1 < l) break;
            int y = 0;
            if (size - 1 == l) { y = l; }
            else if (Compare(keys[l], keys[r]) == 1) { y = r; }
            else { y = l; }
            if (Compare(keys[y], k) > 0) break;
            keys[x] = keys[y];
            values[x] = values[y];
            x = y;
        }
        keys[x] = k;
        values[x] = v;
    }
    public Tvalue Take() { Tvalue ret = values[0]; Poll(); return ret; }
    public Tvalue Peek() { return values[0]; }
    public void Debug()
    {
        Console.Write("key   : ");
        foreach (var k in keys) Console.Write(k + " ");
        Console.WriteLine();
        Console.Write("value : ");
        foreach (var k in values) Console.Write(k + " ");
        Console.WriteLine();
    }
}
public class Input
{
    private static Queue<string> q = new Queue<string>();
    private static void Confirm() { if (q.Count == 0) foreach (var s in Console.ReadLine().Split(' ')) q.Enqueue(s); }
    public static int NextInt() { Confirm(); return int.Parse(q.Dequeue()); }
    public static long NextLong() { Confirm(); return long.Parse(q.Dequeue()); }
    public static char NextChar() { Confirm(); return char.Parse(q.Dequeue()); }
    public static string NextString() { Confirm(); return q.Dequeue(); }
    public static double NextDouble() { Confirm(); return double.Parse(q.Dequeue()); }
    public static int[] LineInt() { return Console.ReadLine().Split(' ').Select(int.Parse).ToArray(); }
    public static long[] LineLong() { return Console.ReadLine().Split(' ').Select(long.Parse).ToArray(); }
    public static string[] LineString() { return Console.ReadLine().Split(' ').ToArray(); }
    public static double[] LineDouble() { return Console.ReadLine().Split(' ').Select(double.Parse).ToArray(); }
}