Contest Duration: - (local time) (100 minutes) Back to Home
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Time Limit: 2 sec / Memory Limit: 256 MB

### 問題文

このままでは、高橋君たち全員を椅子に座らせることができないかもしれません。 高橋君たちの健康管理に気を遣っている青木君は、椅子をできるだけ少ない数追加することで、 高橋君たち全員のこだわりを満たすように高橋君たちを椅子に座らせることができるようにしたいです。

### 制約

• 1 ≦ N,M ≦ 2 × 10^5
• 0 ≦ L_i < R_i ≦ M + 1(1 ≦ i ≦ N)
• 入力は全て整数である

### 入力

N M
L_1 R_1
:
L_N R_N


### 入力例 1

4 4
0 3
2 3
1 3
3 4


### 出力例 1

0


4 人の高橋君を順に座標 3,2,1,4 にある椅子に座らせることができるため、椅子を追加する必要はありません。

### 入力例 2

7 6
0 7
1 5
3 6
2 7
1 6
2 6
3 7


### 出力例 2

2


### 入力例 3

3 1
1 2
1 2
1 2


### 出力例 3

2


### 入力例 4

6 6
1 6
1 6
1 5
1 5
2 6
2 6


### 出力例 4

2


Score : 1000 points

### Problem Statement

There are M chairs arranged in a line. The coordinate of the i-th chair (1 ≤ i ≤ M) is i.

N people of the Takahashi clan played too much games, and they are all suffering from backaches. They need to sit in chairs and rest, but they are particular about which chairs they sit in. Specifically, the i-th person wishes to sit in a chair whose coordinate is not greater than L_i, or not less than R_i. Naturally, only one person can sit in the same chair.

It may not be possible for all of them to sit in their favorite chairs, if nothing is done. Aoki, who cares for the health of the people of the Takahashi clan, decides to provide additional chairs so that all of them can sit in chairs at their favorite positions.

Additional chairs can be placed at arbitrary real coordinates. Find the minimum required number of additional chairs.

### Constraints

• 1 ≤ N,M ≤ 2 × 10^5
• 0 ≤ L_i < R_i ≤ M + 1(1 ≤ i ≤ N)
• All input values are integers.

### Input

Input is given from Standard Input in the following format:

N M
L_1 R_1
:
L_N R_N


### Output

Print the minimum required number of additional chairs.

### Sample Input 1

4 4
0 3
2 3
1 3
3 4


### Sample Output 1

0


The four people can sit in chairs at the coordinates 3, 2, 1 and 4, respectively, and no more chair is needed.

### Sample Input 2

7 6
0 7
1 5
3 6
2 7
1 6
2 6
3 7


### Sample Output 2

2


If we place additional chairs at the coordinates 0 and 2.5, the seven people can sit at coordinates 0, 5, 3, 2, 6, 1 and 2.5, respectively.

### Sample Input 3

3 1
1 2
1 2
1 2


### Sample Output 3

2


### Sample Input 4

6 6
1 6
1 6
1 5
1 5
2 6
2 6


### Sample Output 4

2