Problem:
Longest Increasing Subsequence

For a given sequence A = {a0, a1, ... , an-1}, find the length of the longest increasing subsequnece (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 ≤ 109

Sample Input 1

5
5
1
3
2
4

Sample Output 1

3

Sample Input 2

3
1
1
1

Sample Output 2

1

Solution in Python3 (judge verdict: Runtime Error)

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)