Problem:
Longest Increasing Subsequence

For a given sequence A = {a0, a1, ... , an-1}, find the length of the longest increasing subsequnece (LIS) in A.

An increasing subsequence of A is defined by a subsequence {ai0, ai1, ... , aik} where 0 ≤ i0 < i1 < ... < ik < n and ai0 < ai1 < ... < aik.

Input

n
a0
a1
:
an-1

In the first line, an integer n is given. In the next n lines, elements of A are given.

Output

The length of the longest increasing subsequence of A.

Constraints

1 ≤ n ≤ 100000

0 ≤ ai ≤ 109

Sample Input 1

5
5
1
3
2
4

Sample Output 1

3

Sample Input 2

3
1
1
1

Sample Output 2

1

Solution in Haskell (judge verdict: Time Limit Exceeded)

import Control.Applicative
import Control.Monad
import Data.Functor
import Data.Array
import Data.List

import qualified Data.ByteString.Char8 as C
import Data.Maybe

main = sol <$> (C.getLine *> get) >>= print

get = fmap fst . mapMaybe C.readInt . C.words <$> C.getLine

sol as = siz $ lis as 
    where
    dp = listArray (0, length as - 1) $ repeat mxb
    lis = foldl' lbd dp
    siz = length . filter (< mxb) . elems

mxb = maxBound :: Int

-- lbd :: (Ix i, Ord e, Integral i) => Array i e -> e -> Array i e
lbd dp a = dp//[(bsearch l r p, a)]
    where
    (l,r) = bounds dp
    p i = dp!i > a

-- Binary search
--bsearch :: Integral t => t -> t -> (t -> Bool) -> t
bsearch l r p -- precondition: (p l) && not (p r)
  | l+1==r    = if p l then l else r
  | p m       = bsearch l m p
  | otherwise = bsearch m r p
  where m = (l+r) `div` 2