Box Nesting

There are n cube-shaped boxes arranged in a row from front to back. Each box has a size.

A box may be placed inside a later box only when the earlier box is smaller than the later box. The order of the boxes cannot be rearranged, so the selected box sizes must form a strictly increasing subsequence.

Given the sizes of the boxes, determine the maximum number of boxes that can be nested into one chain.

The first line contains the number of boxes n (1 <= n <= 1000).

The second line contains the sizes of the boxes in order, separated by spaces. Each size is an integer from 1 to 1000.

Print the maximum number of boxes that can be nested into one chain.