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 (sortBy)
import Data.Function (on)

main = do
  li <- getLine
  let n = read li
  as <- forM [1..n] (\_ -> do
    li <- getLine
    return $ read li
    )
  let ans = compute as
  print ans

compute :: [Int] -> Int
compute = length . loop . initial

initial as = [ [(a,a)] | a <- as ]

loop [x] = x
loop xs = loop (zipWith1 connect xs)

zipWith1 f (x:y:xs) = f x y : zipWith1 f xs
zipWith1 f xs = xs

connect abs cds = merge abs1 cds1 where
  abs1 = sortBy (compare `on` snd) abs
  cds1 = sortBy (compare `on` fst) cds

merge ((a,b):abs) cds1@((c,d):cds)
  | b < c = (a,d) : merge abs cds
  | True  = (a,b) : merge abs cds1
merge abs [] = abs
merge [] cds = cds