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Problems

Longest Ordered Subsequence

Longest Ordered Subsequence

Time limit 1 second
Memory limit 64 MiB

A numeric sequence of a_i is ordered if a_1a_2 ≤ … ≤ a_N. Let the subsequence of the given numeric sequence (a_1, a_2, …, a_N) be any sequence (a_i1, a_i2, …, a_iK), where 1i_1 < i_2 < … < i_KN. For example, the 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 of this sequence are of length 4, e. g., (1, 3, 5, 8).

Your program, when given the numeric sequence, must find the length of its longest ordered subsequence.

Input data

The first line of input file contains the length of sequence N (1N10^5). The second line contains the elements of sequence — N integers in the range from 0 to 10^6 each, separated by spaces.

Output data

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

Examples

Input example #1
7
1 7 3 5 9 4 8
Output example #1
4
Source ACM ICPC 2002/2003 Quarterfinal (Far-Eastern Subregion) Vladivostok, November 2, 2002.