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 Haskell (GHC 7.10.3) (judge verdict: Wrong Answer)


import Control.Monad

foo :: [Int] -> Int -> Int
foo [] num = num
foo (n:ns) color = foo (bar n ns) (color+1) where
  bar _ [] = []
  bar x (c:cs) = if c > x then bar x cs else c:bar x cs

main = do
  n <- read <$> getLine :: IO Int
  ints <- replicateM n (read <$> getLine) :: IO [Int]
  print $ foo ints 0