#############################
# Author: Aravind Kashyap
# File: lis.py
# comments: This programme outputs the Longest Strictly Increasing Subsequence in O(NLogN)
#           Where N is the Number of elements in the list
#############################
def CeilIndex(v, l, r, key):
    while r - l > 1:
        m = (l + r) / 2
        if v[m] >= key:
            r = m
        else:
            l = m

    return r


def LongestIncreasingSubsequenceLength(v):
    if len(v) == 0:
        return 0

    tail = [0] * len(v)
    length = 1

    tail[0] = v[0]

    for i in range(1, len(v)):
        if v[i] < tail[0]:
            tail[0] = v[i]
        elif v[i] > tail[length - 1]:
            tail[length] = v[i]
            length += 1
        else:
            tail[CeilIndex(tail, -1, length - 1, v[i])] = v[i]

    return length


if __name__ == "__main__":
    v = [2, 5, 3, 7, 11, 8, 10, 13, 6]
    print(LongestIncreasingSubsequenceLength(v))