In this assignment you shall implement a rudimentary flight trip planner. The input is the set of flights between various cities. It is given as a file. Each line of the file contains "city1 city2 departure-time arrival-time flight-no. price" This means that there is a flight called "flight-no" (which is a string of the form XY012) from city1 to city2 which leaves city1 at time "departure-time" and arrives city2 at time "arrival-time". Further the price of this flight is "price" which is a poitive integer. All times are given as a string of 4 digits in the 24hr format e.g. 1135, 0245, 2210. Assume that all city names are integers between 1 and a number N (where N is the total number of cities).

Note that there could be multiple flights between two cities (at different times).

The query that you have to answer is: given two cities "A" and "B",
times "t1", "t2", where t1 < t2, find the cheapest trip which leaves
city "A" after time "t1" and arrives at city "B" before time "t2". A
trip is a sequence of flights which starts at A after time t1 and ends
at B before time t2. Further, the departure time from any transit
(intermediate) city C is at least 30 mins after the arrival at C.

Your algorithm should be as efficient as possible.

Sample input file

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7 # no of cities

15 # no of lines with information of one flight in each line.

2 5 1026 1234 AI324 6234 # says that flight AI324 leaves from city 2 at 1026 and reaches city 5 at 1234 and costs Rs 6234

3 7 1221 1456 TG342 543

... # 113 more lines

10 # no of queries to follow, one in each line

3 6 0245 1735 # compute the cheapest trip from city 3 to city 6 which starts after 0245hrs and arrives before 1735.

.... # 9 more queries

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For each query output the price of the cheapest trip (one number only) on one line.

Example output

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34526

34784

73267

....

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