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 Lua (Lua 5.3.5) (judge verdict: Wrong Answer)

local function lower_bound(key,ary)
    local n=#ary
    if n==0 then
        return 1 
    end
    if key<=ary[1] then
        return 1
    end
    if key>ary[n] then
        return n+1
    end
    local min,max=1,n
    while 1<max-min do
        local mid=math.floor((min+max)/2)
        if key>ary[mid] 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")
end

local INF=math.maxinteger
local dp={}
for i=1,n do
    dp[i]=INF
end

local len=0
for i=n,1,-1 do
    local k=lower_bound(a[i],dp)
    dp[k]=a[i]
    len=math.max(k,len)
end
print(len)