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
import           Data.List
main = do
    n <- readLn :: IO Int
    a <- replicateM n readLn :: IO [Int]
    print . length $ solve [] a

solve :: [Int] -> [Int] -> [Int]
solve [] (x:xs) = solve [x] xs
solve zs [] = zs
solve zs (x:xs) =
    case find (\z -> z < x) zs of
        Just i  -> let nzs = changeList i x xs
                    in solve nzs xs
        Nothing -> solve (x:zs) xs

changeList i v =
 map (\(j,x) -> if i == j then v else x) . zip [0..]