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 Fortran (gfortran v4.8.4) (judge verdict: Accepted)

program main
 implicit none
 integer n,val,ind,i,j
 integer, allocatable::a(:)
 read(*,*) n
 allocate(a(1:n))
 do i=1,n
  a(i) = -1
 end do
 read(*,*) val
 ind = 1
 a(1) = val
 do i=2,n
  read(*,*) val
  if(a(ind) >= val) then
   a(ind+1) = val
   ind = ind+1
  else
   do j=1,ind
    if(a(j) < val) then
     a(j) = val
     exit
    end if
   end do
  end if
 end do
 write(*,*) ind
end program main