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 (GCC 5.4.1) (judge verdict: Accepted)

#include<stdio.h>
#include<stdlib.h>
#include<stdint.h>
#include<inttypes.h>

typedef int32_t i32;
typedef int64_t i64;

typedef struct binaryHeap{
  void *array;
  size_t heap_size;
  size_t max_size;
  size_t val_size;
  int (*cmp) (const void *, const void *);
} heap;

heap* new_binary_heap (const size_t val_size, int (*cmpF) (const void *, const void *)) {
  heap *h = (heap *) calloc (1, sizeof (heap));
  h->array = malloc (val_size * (1 + 1));
  h->heap_size = 0;
  h->max_size = 1;
  h->val_size = val_size;
  h->cmp = cmpF;
  return h;
}

int32_t get_heap_size (const heap *h) {
  return h->heap_size;
}

int is_empty (const heap *h) {
  return h->heap_size == 0;
}

void free_heap (heap *h) {
  free (h->array);
  free (h);
}

void init_heap (heap *h) {
  h->heap_size = 0;
}

static inline void heap_func_swap (void * restrict a, void * restrict b, size_t val_size) {
  if ((val_size & 7) == 0) {
    uint64_t *p = (uint64_t *) a;
    uint64_t *q = (uint64_t *) b;
    val_size /= sizeof (uint64_t);
    while (val_size--) {
      const uint64_t tmp = *p;
      *p++ = *q;
      *q++ = tmp;
    }
  } else {
    uint8_t *p = (uint8_t *) a;
    uint8_t *q = (uint8_t *) b;
    while (val_size--) {
      const uint8_t tmp = *p;
      *p++ = *q;
      *q++ = tmp;
    }
  }
}

static inline void heap_func_copy (void * restrict dst, const void * restrict src, size_t val_size) {
  if ((val_size & 7) == 0) {
    const uint64_t *p = (const uint64_t *) src;
    uint64_t *q = (uint64_t *) dst;
    val_size /= sizeof (uint64_t);
    while (val_size--) {
      *q++ = *p++;
    }
  } else {
    const uint8_t *p = (const uint8_t *) src;
    uint8_t *q = (uint8_t *) dst;
    while (val_size--) {
      *q++ = *p++;
    }
  }
}

void push (heap * const h, const void *val) {
  if (h->heap_size == h->max_size) {
    h->max_size = 2 * h->max_size + 1;
    h->array = realloc (h->array, h->val_size * (h->max_size + 1));
  }
  h->heap_size++;
  uint8_t * const array = (uint8_t *) h->array;
  size_t k = h->heap_size;
  const size_t val_size = h->val_size;
  int (* const cmp) (const void *, const void *) = h->cmp;
  heap_func_copy(array + k * val_size, val, val_size);
  while (k > 1) {
    size_t parent = k / 2;
    if (cmp (array + parent * val_size, array + k * val_size) <= 0) {
      return;
    }
    heap_func_swap (array + parent * val_size, array + k * val_size, val_size);
    k = parent;
  }
}

void pop (heap * const h, void *res) {
  uint8_t * const array = (uint8_t *) h->array;
  const size_t val_size = h->val_size;
  if (res != NULL) {
    heap_func_copy (res, array + val_size, val_size);
  }
  heap_func_copy (array + val_size, array + val_size * h->heap_size, val_size);
  h->heap_size--;
  int (* const cmp) (const void *, const void *) = h->cmp;
  const size_t n = h->heap_size;
  size_t k = 1;
  while (2 * k  + 1 <= n) {
    const int c = cmp (array + val_size * 2 * k, array + val_size * (2 * k + 1));
    const size_t next = 2 * k + (c <= 0 ? 0 : 1);
    if (cmp (array + val_size * k, array + val_size * next) <= 0) return;
    heap_func_swap (array + val_size * k, array + val_size * next, val_size);
    k = next;
  }
  if (2 * k <= n && cmp (array + val_size * k, array + val_size * 2 * k) > 0) {
    heap_func_swap (array + val_size * k, array + val_size * 2 * k, val_size);
  }
}

void top (const heap *h, void *res) {
  uint8_t *array = (uint8_t *) h->array;
  const size_t val_size = h->val_size;
  if (res != NULL) {
    heap_func_copy (res, array + val_size, val_size);
  }
}

int cmp_min (const void *a, const void *b) {
  i32 d = *(i32 *)a - *(i32 *)b;
  return d == 0 ? 0 : d < 0 ? -1 : 1;
}

int cmp_max (const void *a, const void *b) {
  return - cmp_min (a, b);
}

void run (void) {
  i32 q;
  scanf ("%" SCNi32, &q);
  heap *small = new_binary_heap (sizeof (i32), cmp_max);
  heap *large = new_binary_heap (sizeof (i32), cmp_min);
  i64 sum_small = 0;
  i64 sum_large = 0;
  i64 sum_b = 0;
  while (q--) {
    i32 op;
    scanf ("%" SCNi32, &op);
    if (op == 1) {
      i32 a, b;
      scanf ("%" SCNi32 "%" SCNi32, &a, &b);
      sum_b += b;
      push (small, &a); sum_small += a;
      push (large, &a); sum_large += a;
      i32 x, y;
      top (small, &x);
      top (large, &y);
      if (x <= y) continue;
      pop (small, &x); sum_small -= x;
      pop (large, &y); sum_large -= y;
      push (small, &y); sum_small += y;
      push (large, &x); sum_large += x;
    } else {
      i32 x;
      top (small, &x);
      i64 f = sum_b + (sum_large - sum_small) / 2;
      printf ("%" PRIi32 " %" PRIi64 "\n", x, f);
    }
  }
}

int main (void) {
  run();
  return 0;
}