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 MaxHeap
  def initialize(&block)
    @array = []
    @score = block
  end

  def insert(key)
    @array.push(key)

    # sifting up
    index = @array.size - 1
    until index == 0
      pindex = (index - 1) / 2
      if (@score.(@array[index]) <=> @score.(@array[pindex])) <= 0
        break
      else
        @array[pindex], @array[index] = @array[index], @array[pindex]
        index = pindex
      end
    end
  end

  alias push insert

  def peek
    if @array.empty?
      fail 'empty'
    end

    @array[0]
  end

  def size
    @array.size
  end

  def empty?
    @array.empty?
  end

  def pop
    if @array.empty?
      fail 'empty'
    end

    top = @array[0]
    last = @array.pop
    if @array.empty?
      return top
    end

    @array[0] = last
    i = 0
    # sifting down
    while true
      break unless i*2 + 1 < @array.size

      if i*2 + 2 < @array.size &&
         (@score.(@array[i*2 + 1]) <=> @score.(@array[i*2 + 2])) <= 0
        if (@score.(@array[i*2 + 2]) <=> @score.(@array[i])) <= 0
          break
        else
          @array[i], @array[i*2 + 2] = @array[i*2 + 2], @array[i]
          i = i*2 + 2
        end
      else
        fail "logic error" unless i*2 + 1 < @array.size
        if (@score.(@array[i*2 + 1]) <=> @score.(@array[i])) <= 0
          break
        else
          @array[i], @array[i*2 + 1] = @array[i*2 + 1], @array[i]
          i = i*2 + 1
        end
      end
    end

    return top
  end
end

q = gets.to_i
queries = q.times.map { gets.split.map(&:to_i) }

ql = MaxHeap.new { |v| v }
qr = MaxHeap.new { |v| -v }
minimum = 0

queries.each do |type, a, b|
  case type
  when 1
    left = ql.size == 0 ? -Float::INFINITY : ql.peek
    right = qr.size == 0 ? Float::INFINITY : qr.peek

    if ql.size < qr.size
      ql.push(a)
      ql.push(a)
    elsif ql.size > qr.size
      qr.push(a)
      qr.push(a)
    else
      ql.push(a)
      qr.push(a)
    end

    if a.between?(left, right)
    else
      minimum += [left - a, right - a].map(&:abs).min
    end

    minimum += b
  when 2
    x = ql.peek
    puts "#{x} #{minimum}"
  end
end