## IOI '16 P2 - Railroads (Standard I/O)

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Points: 40 (partial)
Time limit: 1.0s
Memory limit: 256M

Problem types

Anna is working in an amusement park and she is in charge of building the railroad for a new roller coaster. She has already designed special sections (conveniently numbered from to ) that affect the speed of a roller coaster train. She now has to put them together and propose a final design of the roller coaster. For the purpose of this problem you may assume that the length of the train is zero.

For each between and , inclusive, the special section has two properties:

• when entering the section, there is a speed limit: the speed of the train must be less or equal to km/h (kilometers per hour),
• when leaving the section, the speed of the train is exactly km/h, regardless of the speed at which the train entered the section.

The finished roller coaster is a single railroad line that contains the special sections in some order. Each of the sections should be used exactly once. Consecutive sections are connected with tracks. Anna should choose the order of the sections and then decide the lengths of the tracks. The length of a track is measured in meters and may be equal to any non-negative integer (possibly zero).

Each meter of the track between two special sections slows the train down by km/h. At the beginning of the ride, the train enters the first special section in the order selected by Anna, going at km/h.

The final design must satisfy the following requirements:

• the train does not violate any speed limit when entering the special sections;
• the speed of the train is positive at any moment.

In all subtasks except subtask 3, your task is to find the minimum possible total length of tracks between sections. In subtask 3 you only need to check whether there exists a valid roller coaster design, such that each track has zero length.

#### Input Specification

Line of input will contain a single integer , the number of elements in and (i.e., the number of special sections).
Line will each contain two space seperated integers and , the maximum allowed entry speed and exit speed of the th special section, respectively.

#### Output Specification

For all subtasks except 3: a single integer representing denoting the minimum length of tracks.
For subtask 3: a single integer 0 if there is a design with zero length, or any positive integer if it does not exist.

4
1 7
4 3
5 8
6 6

3

#### Explanation for Sample Output

In this example there are four special sections. The best solution is to build them in the order , and to connect them by tracks of lengths respectively.
This is how a train travels along this railroad track:

• Initially the speed of the train is km/h.
• The train starts the ride by entering special section .
• The train leaves section going at km/h.
• Then there is a track of length m. When the train reaches the end of the track, its speed is km/h.
• The train enters special section going at km/h and leaves it at the same speed.
• After leaving section , the train travels along a m long track. Its speed decreases to km/h.
• The train enters special section going at km/h and leaves it going at km/h.
• Immediately after special section the train enters special section .
• The train leaves section . Its final speed is km/h.

Your program should output the total length of tracks between the special sections: