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 Ruby (2.3.3) (judge verdict: Wrong Answer)

class PriorityQueue
  attr_accessor :data, :compare, :compare_method_name

  def initialize(array = [], compare_proc = nil)
    @data = []
    array.each { |a| push(a) }
    @compare_proc = compare_proc
    @compare = "small_compare"
  end

  def change_to_bigger
    @compare = "large_compare"
  end

  def push(element)
    current = @data.size
    while current > 0
      p = parent(current)
      break if compare_equal(@data[p], element)
      @data[current] = @data[p]
      current = p
    end
    @data[current] = element
  end

  def pop
    ret = @data[0]
    x = @data[-1]
    current = 0
    while have_child?(current)
      a = left_child(current)
      b = right_child(current)
      a = b if b < @data.size - 1 && compare(@data[b], @data[a])
      break if compare_equal(x, @data[a])
      @data[current] = @data[a]
      current = a
    end
    @data[current] = x
    @data.pop

    ret
  end

  def front
    @data[0]
  end

  def empty?
    @data.empty?
  end

  def size
    @data.size
  end

  private
  def parent(num)
    (num - 1) / 2
  end

  def left_child(num)
    num * 2 + 1
  end

  def right_child(num)
    num * 2 + 2
  end

  def have_child?(num)
    left_child(num) < @data.size - 1
  end

  def small_compare(a, b)
    a < b
  end

  def large_compare(a, b)
    a > b
  end

  def compare(a, b)
    return @compare_proc.call(a, b) unless @compare_proc.nil?
    send(@compare, a, b)
  end

  def compare_equal(a, b)
    return true if a == b
    compare(a, b)
  end
end

def add(a, b)
  add_value_flg = @large.size == @small.size || @small.size == 0 || a < @small.front || @current < a
  if @small.size == @large.size
    if a < @current
      @large.push(@current)
      @small.push(a)
      @current = @small.pop
    else
      @large.push(a)
    end
  else
    if a < @current
      @small.push(a)
    else
      @small.push(@current)
      @large.push(a)
      @current = @large.pop
    end
  end
  @value += (@current - a).abs + b
  @value += @large.front - @current if add_value_flg
end

N = gets.chomp.to_i

@small = PriorityQueue.new
@small.change_to_bigger
@large = PriorityQueue.new

query = gets.chomp.split.map(&:to_i)
@current = query[1]
@value = query[2]

(N - 1).times do
  query = gets.chomp.split.map(&:to_i)
  if query[0] == 1
    add(query[1], query[2])
  else
    puts "#{@current} #{@value}"
  end
end