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E - Sequence Decomposing /

Time Limit: 2 sec / Memory Limit: 1024 MB

### 問題文

N 個の整数からなる数列 A = \{ A_1, A_2, \cdots, A_N \} が与えられます。 N 個それぞれの整数に対して、色を 1 つ選んでその色を塗ります。 この時、以下の条件を満たす必要があります:

• A_iA_j (i < j) が同じ色で塗られているならば A_i < A_j が成立する

### 制約

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

N
A_1
:
A_N

5
2
1
4
5
3

2

4
0
0
0
0

### 出力例 2

4

Score : 500 points

### 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

### Input

Input is given from Standard Input in the following format:

N
A_1
:
A_N

### Output

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

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.

4
0
0
0
0

### Sample Output 2

4

We have to paint all the integers with distinct colors.