Bus Route Travel Time

You are given a transport network of bus stops and bus routes. Your task is to determine the minimum travel time between two specified stops in the network. The travel time along a route is given and you must use these routes to travel from a start stop to a destination stop.

Formally, consider a directed graph \(G=(V,E)\), where \(V\) represents the bus stops and \(E\) represents the bus routes. Each edge \((u, v)\) has a weight \(w(u,v)\) representing the travel time. The goal for each query is to compute the minimum travel time from a given start stop \(s\) to an end stop \(t\) such that:

[ d(s,t)=\min_{path,s\to t} \sum_{(u,v)\in path} w(u,v) ]

If no path exists, output IMPOSSIBLE.

You are required to read the input from stdin and write the output to stdout.

inputFormat

The input is given in the following format:

S
stop_1 stop_2 ... stop_S
R
origin_1 destination_1 time_1
origin_2 destination_2 time_2
... 
origin_R destination_R time_R
Q
query_start_1 query_end_1
query_start_2 query_end_2
...
query_start_Q query_end_Q

Where:

• S is the number of bus stops.
• The second line contains S bus stop names separated by spaces.
• R is the number of bus routes.
• Each of the next R lines represents a bus route from an origin to a destination with the travel time (an integer).
• Q is the number of queries.
• Each of the next Q lines contains two bus stop names representing the query from a start stop to an end stop.

outputFormat

For each query, output on a new line the minimum travel time between the two stops. If no route exists, output IMPOSSIBLE.

## sample

5
StopA StopB StopC StopD StopE
6
StopA StopB 10
StopB StopC 20
StopC StopD 15
StopD StopE 25
StopA StopC 30
StopA StopE 60
5
StopA StopD
StopC StopE
StopA StopE
StopD StopA
StopB StopA

45
40
60
IMPOSSIBLE
IMPOSSIBLE

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