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 <string.h>
#include <stdlib.h>

#define BUF_SIZE 20

// size: specify sizeof(str)
int get_str(char *str, int size) {
    if(!fgets(str, size, stdin)) return -1;
    return 0;
}

int get_int(void) {
  int num;
#ifdef BUF_SIZE
  char line[BUF_SIZE];
  if(!fgets(line, BUF_SIZE, stdin)) return 0;
  sscanf(line, "%d", &num);
#else
#error
#endif
  return num;
}

#define ARR_MAX 100000

static int stack[ARR_MAX];
static int pos = 0;

void push(int val) {
    stack[pos++] = val;
}

int get_size(void) { return pos; }

// arr: monotonous decrease sequence
int upper_bound(int *arr, int size, int key) {
    int low = size;
    int high = -1;
    while(high + 1 < low) {
        int mid = (low + high)/2;
        if(arr[mid] < key) {
            low = mid;
        } else { 
            high = mid;
        }
#ifdef DEBUG
        printf("judge; %d, %d<%d\n", mid, arr[mid],key);
#endif
    }
    return low;
}

int main(void) {
    int num = get_int();
    static int arr[ARR_MAX];
    int i;
    for(i = 0; i < num; i++) {
        arr[i] = get_int();
    }

    push(arr[0]);
    for(i = 1; i < num; i++) {
        int key = arr[i];
        int idx = upper_bound(stack, get_size(), key);
#ifdef DEBUG
        printf("key: %d -> idx: %d\n", key, idx);
#endif
        // push or update
        if(idx == get_size()) {
            push(key);
        } else {
            stack[idx] = key;
        }
    }
    printf("%d\n", get_size());
    return 0;
}