A numeric sequence of ai is ordered if a1 < a2 < ... < aN.
Let the subsequence of the given numeric sequence (a1, a2, ..., aN) be any sequence (ai1, ai2, ..., aiK)
where 1 <= i1 < i2 < ... < iK <= N.
Your program, when given the numeric sequence, must find the length of its longest ordered subsequence.
The first line of input file contains the length of sequence N.
The second line contains the elements of sequence - N integers, separated by spaces.
1 <= N <= 1000000
Process to the end of file.
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 8Sample Output