#############################
# 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))