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.

Input

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

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

Author

windy7926778