#2339 Longest Ordered Subsequence 2

12  1 s   128 MB  

Description

A numeric sequence of ai is ordered if a1 < a2 < ... < aN. Let the subsequence of the given numeric sequence (a1a2, ..., aN) be any sequence (ai1ai2, ..., aiK), where 1 <= i1 < i2 < ... < iK <= N. For example, sequence (1, 7, 3, 5, 9, 4, 8) has ordered subsequences, e. g., (1, 7), (3, 4, 8) and many others. All longest ordered subsequences are of length 4, e. g., (1, 3, 5, 8).

Input

The first line of input file contains the length of sequence N. The second line contains the elements of sequence - N integers in the range from 0 to 1,000,000 each, separated by spaces. 1 <= N <= 100,000

Output

Output file must contain a single integer - the length of the longest ordered subsequence of the given sequence.

Sample Input

Sample Output

7
1 7 3 5 9 4 8
4

HINT

O( N lg N ) algorithm is needed