CF1773F Football

Scientists are researching an impact of football match results on the mood of football fans. They have a hypothesis that there is a correlation between the number of draws and fans' desire to watch football matches in the future. In football, two teams play a match. The teams score goals throughout a match. A score " $ x $ : $ y $ " means that the team we observe scored $ x $ goals and conceded $ y $ goals. If $ x = y $ , then the match ends in a draw. If $ x > y $ , then the observed team wins, and if $ x < y $ , then it loses. To find out if there is a correlation, the scientists gathered information about the results of teams in lower leagues. The information they found is the number of matches played by the team ( $ n $ ), the number of goals scored in these matches ( $ a $ ), and the number of goals conceded in these matches ( $ b $ ). You are given this information for a single team. You are asked to calculate the minimum number of draws that could have happened during the team's matches and provide a list of match scores with the minimum number of draws.

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