There are people testing their racing cars on notorious *autobahn* where limits do not exist. In this task
however limits do exist. So we kindly ask you to restrain yourself from submitting exponential complexity
solutions.

Person came to *autobahn* at the beginning of minute , paid for minutes of stay and left at the end of
minute . Unfortunately some stayed for longer than that they have paid for. Administration of *autobahn*
decided not to be very harsh and charge them only for those extra minutes in which there were at least
people on *autobahn*.

In a rush of generosity, administration decided to introduce *happy hour* i.e. interval of continuous
minutes for which they won't be paying extra charges. They picked *happy hour* so that the sum of extra
charges that won't be paid is maximal possible. Determine that sum.

#### Input Specification

First line contains integers and from task description.

Next lines contain integers and from task description.

#### Output Specification

Print the required sum in a single line.

#### Scoring

Subtask | Points | Constraints |
---|---|---|

, |

#### Sample Input 1

```
5 3 4
2 1 4
3 3 7
3 3 8
1 5 7
5 3 8
```

#### Sample Output 1

`7`

#### Explanation for Sample Output 1

*Happy hour* will span from 4th until the 7th minute. Inside that interval,
first person should've paid extra for the 4th minute and second, third and fourth person should've paid
for 6th and 7th minute.

#### Sample Input 2

```
3 2 22
7 16 33
69 14 88
8 10 97
```

#### Sample Output 2

`27`

## Comments