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: Time Limit Exceeded)

class PQueue
  def initialize(&block)
    @compare_fn = block || lambda { |x, y| (x <=> y) == -1 }
    @heap = []
  end

  def push(val)
    i = @heap.size

    while i > 0
      p = (i - 1) / 2
      break if compare(@heap[p], val)
      @heap[i] = @heap[p]
      i = p
    end

    @heap[i] = val
  end

  def pop
    val = @heap[0]
    n = @heap.pop
    unless @heap.empty?
      @heap[0] = n
      heapify(0)
    end
    val
  end

  def size
    @heap.size
  end

  def empty?
    @heap.empty?
  end

  def peek
    @heap[0]
  end

  private

  def heapify(i)
    left_idx = i * 2 + 1
    right_idx = i * 2 + 2

    next_idx = i

    next_idx = left_idx if left_idx < @heap.size && compare(@heap[left_idx], @heap[i])
    next_idx = right_idx if right_idx < @heap.size && compare(@heap[right_idx], @heap[next_idx])

    if i != next_idx
      @heap[i], @heap[next_idx] = @heap[next_idx], @heap[i]
      heapify(next_idx)
    end
  end

  def compare(x, y)
    @compare_fn.call(x, y)
  end
end

N = gets.chomp.to_i

left = PQueue.new { |x, y| (x <=> y) == 1 }
right = PQueue.new

query = gets.chomp.split.map(&:to_i)

value = query[2]

left.push(query[1])
right.push(query[1])

(N - 1).times do
  query = gets.chomp.split.map(&:to_i)
  if query[0] == 1
    value += query[2]

    value += left.peek - query[1] if query[1] < left.peek
    value += query[1] - right.peek if right.peek < query[1]

    left.push(query[1])
    right.push(query[1])

    l_max = left.pop
    r_min = right.pop
    left.push(r_min)
    right.push(l_max)
  else
    puts "#{left.peek} #{value}"
  end
end