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: Wrong Answer)

program sequence_decomposing
    implicit none
    integer(4):: n,i,c,cmax
    integer(8):: a1,a2

    read*,n
    read*,a1
    c=0
    cmax=0
    do i=1,n-1
        read*, a2

        if (a2 <= a1)then
            c=c+1
        else
            c=0
        end if
        cmax=max(cmax,c)
        a1=a2
    end do

    print*,cmax+1




end program sequence_decomposing