Two Contests

10^9 contestants, numbered 1 to 10^9, will compete in a competition. There will be two contests in this competition.

The organizer prepared N problems, numbered 1 to N, to use in these contests. When Problem i is presented in a contest, it will be solved by all contestants from Contestant L_i to Contestant R_i (inclusive), and will not be solved by any other contestants.

The organizer will use these N problems in the two contests. Each problem must be used in exactly one of the contests, and each contest must have at least one problem.

The joyfulness of each contest is the number of contestants who will solve all the problems in the contest. Find the maximum possible total joyfulness of the two contests.

Constraints

• 2 \leq N \leq 10^5
• 1 \leq L_i \leq R_i \leq 10^9
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N L_1 R_1 L_2 R_2 \vdots L_N R_N

Output

Print the maximum possible total joyfulness of the two contests.

Examples

Input

4 4 7 1 4 5 8 2 5

Output

6

Input

4 1 20 2 19 3 18 4 17

Output

34

Input

10 457835016 996058008 456475528 529149798 455108441 512701454 455817105 523506955 457368248 814532746 455073228 459494089 456651538 774276744 457667152 974637457 457293701 800549465 456580262 636471526

Output

540049931

inputFormat

input are integers.

Input

Input is given from Standard Input in the following format:

N L_1 R_1 L_2 R_2 \vdots L_N R_N

outputFormat

Output

Print the maximum possible total joyfulness of the two contests.

Examples

Input

4 4 7 1 4 5 8 2 5

Output

6

Input

4 1 20 2 19 3 18 4 17

Output

34

Input

10 457835016 996058008 456475528 529149798 455108441 512701454 455817105 523506955 457368248 814532746 455073228 459494089 456651538 774276744 457667152 974637457 457293701 800549465 456580262 636471526

Output

540049931

样例

4
1 20
2 19
3 18
4 17

34