{"raw_statement":[{"iden":"statement","content":"While you were at science olympiad, you missed your favorite basketball team's biggest game of the year. You don't know the score, but you know the number of baskets, three-pointers, and free throws made by each team. Your task is to figure out which team won the game based on the given information. Recall that a three-pointer is worth 3 points, a regular basket is worth 2 points, and a free throw is worth one point. The number of baskets made includes three-pointers and two-pointers, but not free throws.\n\nThe first line of input contains two space-separated strings: the names of the two teams that played in the basketball game. The second line of input contain two space-separated integers representing the number of baskets made by each team, respectively. The third line of input contain two space-separated integers representing the number of three-pointers made by each team, respectively. The fourth line of input contain two space-separated integers representing the number of free throws made by each team, respectively.\n\nOutput a single string: the team that won the game. It is guaranteed that there is a winner, i.e. the score at the end of the game is not a tie.\n\nIn the example, Syracuse scored 95 points, and Duke scored 91 points. This game occurred on January 14, 2019.\n\n"},{"iden":"input","content":"The first line of input contains two space-separated strings: the names of the two teams that played in the basketball game. The second line of input contain two space-separated integers representing the number of baskets made by each team, respectively. The third line of input contain two space-separated integers representing the number of three-pointers made by each team, respectively. The fourth line of input contain two space-separated integers representing the number of free throws made by each team, respectively."},{"iden":"output","content":"Output a single string: the team that won the game. It is guaranteed that there is a winner, i.e. the score at the end of the game is not a tie."},{"iden":"note","content":"In the example, Syracuse scored 95 points, and Duke scored 91 points. This game occurred on January 14, 2019."}],"translated_statement":null,"sample_group":[],"show_order":[],"formal_statement":"**Definitions**  \nLet $ T_1, T_2 $ be the two team names.  \nLet $ b_1, b_2 \\in \\mathbb{Z}_{\\geq 0} $ be the number of baskets made by $ T_1 $ and $ T_2 $, respectively.  \nLet $ t_1, t_2 \\in \\mathbb{Z}_{\\geq 0} $ be the number of three-pointers made by $ T_1 $ and $ T_2 $, respectively.  \nLet $ f_1, f_2 \\in \\mathbb{Z}_{\\geq 0} $ be the number of free throws made by $ T_1 $ and $ T_2 $, respectively.  \n\n**Constraints**  \n1. $ b_i \\geq t_i $ for $ i \\in \\{1,2\\} $ (baskets include three-pointers)  \n2. All values are non-negative integers.  \n3. Final scores are unequal.  \n\n**Objective**  \nCompute the score for each team:  \n$$\nS_i = 2(b_i - t_i) + 3t_i + f_i = 2b_i + t_i + f_i \\quad \\text{for } i \\in \\{1,2\\}\n$$  \nOutput the team name with the higher score.","simple_statement":"Given the number of baskets, three-pointers, and free throws for two teams, calculate each team's total score and output the name of the winning team.  \n- Each basket = 2 points  \n- Each three-pointer = 3 points  \n- Each free throw = 1 point  \n- Baskets include both 2-pointers and 3-pointers, so subtract three-pointers from baskets to get 2-pointers.  \n- The winner has more points — no ties.","has_page_source":false}