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 LuaJIT (2.0.4) (judge verdict: Accepted)

local mce, mfl, msq, mmi, mma = math.ceil, math.floor, math.sqrt, math.min, math.max
local function upper_bound(ary, x)
  local num = #ary
  if num == 0 then return 1 end
  if(x < ary[1]) then return 1 end
  if(ary[num] <= x) then return num + 1 end
  local min, max = 1, num
  while(1 < max - min) do
    local mid = mfl((min + max) / 2)
    if(ary[mid] <= x) then
      min = mid
    else
      max = mid
    end
  end
  return max
end

local n = io.read("*n")
local a = {}
for i = 1, n do
  a[i] = io.read("*n")
  a[i] = -a[i]
end
local t = {a[1]}
for i = 2, n do
  local pos = upper_bound(t, a[i])
  if i - 1 < pos then
    table.insert(t, a[i])
  else
    t[pos] = a[i]
  end
end
print(#t)