Problem Statement

You are given a sequence with N integers: A = \{ A_1, A_2, \cdots, A_N \}. For each of these N integers, we will choose a color and paint the integer with that color. Here the following condition must be satisfied:

• If A_i and A_j (i < j) are painted with the same color, A_i < A_j.

Find the minimum number of colors required to satisfy the condition.

Constraints

• 1 \leq N \leq 10^5
• 0 \leq A_i \leq 10^9

Sample Input 1

5
2
1
4
5
3

Sample Output 1

2

We can satisfy the condition with two colors by, for example, painting 2 and 3 red and painting 1, 4, and 5 blue.

Sample Input 2

4
0
0
0
0

Sample Output 2

4

We have to paint all the integers with distinct colors.