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 Python (3.4.3) (judge verdict: Runtime Error)


a = int(input())
l = []
for i in range(a):
	t = int(input())
	l.append(t)
d=[False]*a

#a = 5
#l = [2,1,4,5,3]
used=[False]*(a+10)
res =0
for i in range(a):
	if not used[i] and i+1<a:
		f = l[i]
		#print(1,f)
		L = []
		L.append(f)
		res +=1
		used[l[i]] = True
		for j in range(i+1,a):
			if f < l[j] and not used[l[j]]:
				f = l[j]
				#print(f)
				L.append(f)
				used[l[j]] = True
		#print(L)
print(res)