Problem:
Score : 500 points

Problem Statement

You are given a sequence with N integers: A = \{ A_1, A_2, \cdots, A_N \}.
For each of these N integers, we will choose a color and paint the integer with that color. Here the following condition must be satisfied:

If A_i and A_j (i < j) are painted with the same color, A_i < A_j.

Find the minimum number of colors required to satisfy the condition.

Constraints

1 \leq N \leq 10^5

0 \leq A_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N
A_1
:
A_N

Output

Print the minimum number of colors required to satisfy the condition.

Sample Input 1

5
2
1
4
5
3

Sample Output 1

2

We can satisfy the condition with two colors by, for example, painting 2 and 3 red and painting 1, 4, and 5 blue.

Sample Input 2

4
0
0
0
0

Sample Output 2

4

We have to paint all the integers with distinct colors.

Solution in C (GCC 5.4.1) (judge verdict: Accepted)

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

typedef int32_t i32;
typedef int64_t i64;

#define MAX(a,b) ((a)>(b)?(a):(b))
#define MIN(a,b) ((a)<(b)?(a):(b))
#define ABS(a) ((a)>(0)?(a):-(a))
#define ALLOC(size,type) ((type*)calloc((size),sizeof(type)))
#define SORT(a,num,cmp) qsort((a),(num),sizeof(*(a)),cmp)

typedef struct segment_tree_void {
  void *array;
  int32_t size;
  size_t val_size;
  void (*func) (void *, const void *, const void *);
} segment_tree;

static inline void segment_tree_memcpy (void *dst, const void *src, size_t size) {
  uint8_t *p = dst;
  const uint8_t *q = src;
  while (size--) {
    *p++ = *q++;
  }
}

segment_tree* new_segment_tree (const void *ini, const int32_t n, const size_t val_size, void (*func) (void *, const void *, const void *)) {
  int32_t k = 1;
  while (k < n) k *= 2;
  segment_tree *s = (segment_tree *) calloc (1, sizeof (segment_tree));
  s->array = calloc (2 * k, val_size);
  s->size = k;
  s->val_size = val_size;
  s->func = func;
  for (int32_t i = k; i < 2 * k; ++i) {
    segment_tree_memcpy ((uint8_t *)s->array + i * val_size, ini, val_size);
  }
  uint8_t *a = s->array;
  for (int32_t i = k - 1; i > 0; --i) {
    func (a + i * val_size, a + (2 * i) * val_size, a + (2 * i + 1) * val_size);
  }
  return s;
}

void update (segment_tree * const s, int32_t k, const void *val) {
  k += s->size;
  uint8_t * const p = s->array;
  const size_t size = s->val_size;
  segment_tree_memcpy (p + k * size, val, size);
  for (k >>= 1; k > 0; k >>= 1) {
    s->func (p + k * size, p + 2 * k * size, p + (2 * k + 1) * size);
  }
}

void update_tmp (segment_tree * const s, int32_t k, const void *val) {
  k += s->size;
  uint8_t * const p = s->array;
  const size_t size = s->val_size;
  segment_tree_memcpy (p + k * size, val, size);
}

void update_all (segment_tree * const s) {
  uint8_t * const a = s->array;
  const size_t size = s->val_size;
  for (int32_t i = s->size - 1; i > 0; --i) {
    s->func (a + i * size, a + (2 * i) * size, a + (2 * i + 1) * size);
  }
}

void find (const segment_tree *s, int32_t l, int32_t r, void *res) {
  int32_t lindex[64];
  int32_t rindex[32];
  int32_t llen = 0;
  int32_t rlen = 0;
  for (l += s->size, r += s->size; l < r; l >>= 1, r >>= 1) {
    if (l & 1) lindex[llen++] = l++;
    if (r & 1) rindex[rlen++] = --r;
  }
  while (rlen > 0) {
    lindex[llen++] = rindex[--rlen];
  }
  const uint8_t *p = s->array;
  segment_tree_memcpy (res, p + lindex[0] * s->val_size, s->val_size);
  for (int32_t i = 1; i < llen; ++i) {
    s->func (res, res, p + lindex[i] * s->val_size);
  }
}

typedef struct node {
  i32 k;
  i32 v;
} node;

void func_max (void *c, const void *a, const void *b) {
  const node *p = a;
  const node *q = b;
  if (p->v == q->v) {
    *(node *)c = p->k < q->k ? *p : *q;
  } else {
    *(node *)c = p->v >= q->v ? *p : *q;
  }
}

void run (void) {
  i32 n;
  scanf ("%" SCNi32, &n);
  const node ini = {n, -1};
  segment_tree *s = new_segment_tree (&ini, n, sizeof (node), func_max);
  for (i32 i = 0; i < n; ++i) {
    i32 a;
    scanf ("%" SCNi32, &a);
    update_tmp (s, i, &(node){i, a});
  }
  update_all (s);
  i32 ans = 0;
  for (;;) {
    node t;
    find (s, 0, n, &t);
    if (t.v == -1) break;
    ans++;
    update (s, t.k, &ini);
    i32 r = t.k;
    i32 v = t.v;
    while (r > 0) {
      find (s, 0, r, &t);
      if (t.v == -1) break;
      if (t.v < v) {
        update (s, t.k, &ini);
        v = t.v;
      }
      r = t.k;
    }
  }
  printf ("%" PRIi32 "\n", ans);
}

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