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: Wrong Answer)

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

typedef struct tree {
	struct tree *l, *r;
	int x;
} tree;

void tadd(tree **t, int x) {
	if (*t == NULL) {
		*t = malloc(sizeof **t);
		(*t)->l = (*t)->r = NULL;
		(*t)->x = x;
	} else if ((*t)->x >= x) {
		tadd(&(*t)->l, x);
	} else {
		tadd(&(*t)->r, x);
	}
}

tree** tfind(tree **t, int x) {
	if (*t == NULL) return NULL;
	if ((*t)->x >= x) return tfind(&(*t)->l, x);

	tree **ot = tfind(&(*t)->r, x);
	if (ot != NULL) return ot;
	return t;
}

void tremove(tree **t) {
	tree *old = *t;
	if ((*t)->l == NULL) {
		*t = (*t)->r;
		free(old);
	} else if ((*t)->r == NULL) {
		*t = (*t)->l;
		free(old);
	} else {
		tree **prev = &(*t)->r;
		while ((*prev)->l != NULL) prev = &(*prev)->l;
		tree *rem = *prev;
		*prev = NULL;
		(*t)->x = rem->x;
		(*t)->r = rem->r;
		free(rem);
	}
}

int main(void) {
	int n;
	scanf("%d", &n);

	tree *t = NULL;
	int cnt = 0;
	for (int i = 0; i < n; i++) {
		int x;
		scanf("%d", &x);
		tree **found = tfind(&t, x);

		if (found != NULL) tremove(found);
		else cnt++;
		tadd(&t, x);
	}

	printf("%d\n", cnt);
	while (t != NULL) tremove(&t);
}