Chef and cities

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Chef likes to travel a lot. Every day Chef tries to visit as much cities as possible. Recently he had a quite a few trips of great Chefland for learning various recipes. Chefland had N cities numbered from 1 to N. People in Chefland are very friendly, friendliness of i-th city is given by Fi. Before starting of each trip, Chef's initial enjoyment is 1 unit. Whenever he visits a city with friend

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