Title: Longest Increasing Subsequence

For a given sequence A = {a0, a1, ... , an-1}, find the length of the longest increasing subsequence (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 ≤ 10^9

Sample Input 1
5
5
1
3
2
4

Sample Output 1
3

Sample Input 2
3
1
1
1

Sample Output 2
1

# Buggy version:
import bisect
a = int(input())
b = [int(input()) in d in range(a)]
c = [b[1]]
for i in b[1:]:
    if c[-1] < i:
        c.append(i)
    else:
        c[bisect.bisect_left(c,i)] = i
        
print(len(c))


# Fixed version:
import bisect
a = int(input())
b = [int(input()) for d in range(a)]
c = [b[0]]
for i in b[1:]:
    if c[-1] < i:
        c.append(i)
    else:
        c[bisect.bisect_left(c,i)] = i
        
print(len(c))

# Buggy version:
from sys import stdin
import bisect
readline = stdin.readline

dp = [-float('inf')]
n = int(readline())
a = (int(readline()) for _ in range(n))
for ai in a:
    if dp[-1] < ai:
        dp.append(ai)
    else:
        dp[bisect.bisect(dp, ai)] = ai
print(len(dp) - 1)

# Fixed version:
from sys import stdin
from bisect import bisect_left
readline = stdin.readline


dp = [-float('inf')]
n = int(readline())
a = (int(readline()) for _ in range(n))
for ai in a:
    if dp[-1] < ai:
        dp.append(ai)
    else:
        dp[bisect_left(dp, ai)] = ai
print(len(dp) - 1)

# Buggy version:
from bisect import bisect_left
import sys
n = int(input())
A = [int(i.rstrip("\n")) for i in sys.stdin.readlines()]

def LIS():
    L = A[:1]
    for i in A[1:]:
        if L[-1] < i:
            L.append(i)
        else:
            L[j] = i
    return len(L)

print(LIS())

# Fixed version:
from bisect import bisect_left
import sys

n = int(input())
A = [int(i.rstrip("\n")) for i in sys.stdin.readlines()]

def LIS():
    L = A[:1]
    for i in A[1:]:
        if L[-1] < i:
            L.append(i)
        else:
            j = bisect_left(L, i)
            L[j] = i
    return len(L)

print(LIS())

# Buggy version:
# -*- coding: utf-8 -*-
from bisect import bisect
N = int(input())
A = [int(input()) for _ in range(N)]
L = [A[0]]

for i in range(1, N):
    if L[-1] < A[i]:
        L.append(A[i])
    else:
        L[bisect(L, A[i])]  = A[i]
print(len(L))

# Fixed version:
# -*- coding: utf-8 -*-
from bisect import bisect_left
N = int(input())
A = [int(input()) for _ in range(N)]
L = [A[0]]

for i in range(1, N):
    if L[-1] < A[i]:
        L.append(A[i])
    else:
        L[bisect_left(L, A[i])]  = A[i]
print(len(L))

# Buggy version:
import bisect
n = int(input())
A = []
for i in range(n):
    num  = int(input())
    if A == []:
        A.append(num)
    elif num > A[-1]:
        A.append(num)
    else:
        j = bisect.bisect_left(A, num)
        A[j] = num
print(len(A) - 1)

# Fixed version:
import bisect
n = int(input())
A = []
for i in range(n):
    num  = int(input())
    if A == []:
        A.append(num)
    elif num > A[-1]:
        A.append(num)
    else:
        j = bisect.bisect_left(A, num)
        A[j] = num
print(len(A))