Source : Northeastern Europe 2002, Far-Eastern Subregion
Description

  A numeric sequence of ai is ordered if a1<a2<...<aNa_1 < a_2 < ... < a_N. Let the subsequence of the given numeric sequence (a1,a2,...,aN)(a_1, a_2, ..., a_N)be any sequence (ai1,ai2,...,aiK)(a_{i1}, a_{i2}, ..., a_{iK}), where 1<=i1<i2<...<iK<=N1 <= i_1 < i_2 < ... < i_K <= N. For example, sequence (1,7,3,5,9,4,8)(1, 7, 3, 5, 9, 4, 8) has ordered subsequences, e. g., (1,7),(3,4,8)(1, 7), (3, 4, 8) and many others. All longest ordered subsequences are of length 44, e. g., (1,3,5,8)(1, 3, 5, 8).
  Your program, when given the numeric sequence, must find the length of its longest ordered subsequence.

Input

  The first line of input file contains the length of sequence NN. The second line contains the elements of sequence - NN integers in the range from 00 to 1000010000 each, separated by spaces. 1<=N<=10001 <= N <= 1000.

Output

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

Sample Input
7
1 7 3 5 9 4 8
Sample Output
4