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.Linq;
using System.Collections.Generic;
using System.Text;

namespace Program
{
    public class ABC127F
    {
        static public void Main(string[] args)
        {
            var Q = NextInt;
            var b = 0L;
            var x = 0L;
            bool first = true;
            var f = 0L;
            var listA = new PQ<long>(false);
            var listB = new PQ<long>();
            var totalCount = 0;
            for (int i = 0; i < Q; ++i)
            {
                var query = NextString;
                if (query[0] == '1')
                {
                    var a = NextLong;
                    b += NextLong;
                    if (first)
                    {
                        first = false;
                        totalCount = 1;
                        listA.Push(a);
                    }
                    else
                    {
                        f += Math.Min(Math.Abs(listA.Peek - a), listB.Count == 0 ? int.MaxValue : Math.Abs(listB.Peek - a));
                        if (a <= x)
                        {
                            if (totalCount % 2 != 0)
                            {
                                listB.Push(listA.Pop);
                            }
                            listA.Push(a);
                        }
                        else
                        {
                            if (totalCount % 2 == 0)
                            {
                                var tmp = listA.Peek;
                                listA.Push(listB.Pop);
                            }
                            listB.Push(a);
                        }
                        ++totalCount;
                    }
                    x = listA.Peek;
                }
                else
                {
                    Console.WriteLine(x + " " + (f + b));
                }
            }
        }

        static class Console_
        {
            private static Queue<string> param = new Queue<string>();
            public static string NextString()
            {
                if (param.Count == 0) foreach (var item in Console.ReadLine().Split(' ')) param.Enqueue(item);
                return param.Dequeue();
            }
        }
        static int NextInt => int.Parse(Console_.NextString());
        static List<int> NextIntList(int N)
        {
            var ret = new List<int>(N);
            for (int i = 0; i < N; ++i) ret.Add(NextInt);
            return ret;
        }
        static long NextLong => long.Parse(Console_.NextString());
        static List<long> NextLongList(int N)
        {
            var ret = new List<long>(N);
            for (int i = 0; i < N; ++i) ret.Add(NextLong);
            return ret;
        }
        static string NextString => Console_.NextString();
        static void Sort<T>(List<T> l) where T : IComparable => l.Sort();
        static void RevSort<T>(List<T> l) where T : IComparable => l.Sort((x, y) => y.CompareTo(x));
        static IEnumerable<long> Prime(long x)
        {
            if (x < 2) yield break;
            yield return 2;
            var halfx = x / 2;
            var table = new bool[halfx + 1];
            var max = (long)(Math.Sqrt(x) / 2);
            for (long i = 1; i <= max; ++i)
            {
                if (table[i]) continue;
                var add = 2 * i + 1;
                yield return add;
                for (long j = 2 * i * (i + 1); j <= halfx; j += add) table[j] = true;
            }
            for (long i = max + 1; i <= halfx; ++i) if (!table[i]) yield return 2 * i + 1;
        }
        static IEnumerable<long> Divisor(long x)
        {
            if (x < 1) yield break;
            var max = (long)Math.Sqrt(x);
            for (long i = 1; i < max; ++i)
            {
                if (x % i != 0) continue;
                yield return i;
                if (i != x / i) yield return x / i;
            }
        }
        static long GCD(long a, long b)
        {
            long tmpa = a, tmpb = b;
            while (tmpb > 0) { var tmp = tmpb; tmpb = tmpa % tmpb; tmpa = tmp; }
            return tmpa;
        }
        class PQ<T> where T : IComparable
        {
            private List<T> h;
            private Comparison<T> c;
            public PQ(int cap, Comparison<T> c, bool asc = true) { h = new List<T>(cap); this.c = asc ? c : (x, y) => c(y, x); }
            public PQ(Comparison<T> c, bool asc = true) { h = new List<T>(); this.c = asc ? c : (x, y) => c(y, x); }
            public PQ(int cap, bool asc = true) : this(cap, (x, y) => x.CompareTo(y), asc) { }
            public PQ(bool asc = true) : this((x, y) => x.CompareTo(y), asc) { }
            public void Push(T v)
            {
                var i = h.Count;
                h.Add(v);
                while (i > 0)
                {
                    var ni = (i - 1) / 2;
                    if (c(v, h[ni]) >= 0) break;
                    h[i] = h[ni]; i = ni;
                }
                h[i] = v;
            }
            public T Peek => h[0];
            public int Count => h.Count;
            public T Pop
            {
                get
                {
                    var r = h[0];
                    var v = h[h.Count - 1];
                    h.RemoveAt(h.Count - 1);
                    if (h.Count == 0) return r;
                    var i = 0;
                    while (i * 2 + 1 < h.Count)
                    {
                        var i1 = i * 2 + 1;
                        var i2 = i * 2 + 2;
                        if (i2 < h.Count && c(h[i1], h[i2]) > 0) i1 = i2;
                        if (c(v, h[i1]) <= 0) break;
                        h[i] = h[i1]; i = i1;
                    }
                    h[i] = v;
                    return r;
                }
                private set { }
            }
        }
        class PQ<TKey, TValue> where TKey : IComparable
        {
            private PQ<Tuple<TKey, TValue>> q;
            public PQ(int cap, Comparison<TKey> c, bool asc = true) { q = new PQ<Tuple<TKey, TValue>>(cap, (x, y) => c(x.Item1, y.Item1), asc); }
            public PQ(Comparison<TKey> c, bool asc = true) { q = new PQ<Tuple<TKey, TValue>>((x, y) => c(x.Item1, y.Item1), asc); }
            public PQ(int cap, bool asc = true) : this(cap, (x, y) => x.CompareTo(y), asc) { }
            public PQ(bool asc = true) : this((x, y) => x.CompareTo(y), asc) { }
            public void Push(TKey k, TValue v) => q.Push(Tuple.Create(k, v));
            public Tuple<TKey, TValue> Peek => q.Peek;
            public int Count => q.Count;
            public Tuple<TKey, TValue> Pop => q.Pop;
        }
    }
}