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Bingo is a game in which players try to form patterns on a 5 x 5 grid (or card). Each column on the card is represented by a letter in the game's namesake: B, I, N, G, or O. Each square on the grid contains a number. Players mark numbers as they are chosen randomly until a person has a card with a winning pattern marked (or bingo). An exception to this is the center square in the grid, which is a free spot and is already marked for all players at the beginning of each game. The possible numbers called are 1-75, inclusive, with each set of fifteen numbers corresponding to a letter: B for 1-15, I for 16-30, N for 31-45, G for 46-60, and O for 61-75.
Given the amount of numbers for each letter already called and information used to determine the set of winning patterns, write a program to determine the fewest amount of numbers that still need to be called for a possible bingo.
Input to this problem will begin with a line containing a single integer n indicating the number of data sets. The first line in each data set will be in the format B I N G O X Y where:
For example, given an X of 4, a Y of 2, and a set of input patterns as follows:
XXOOO OOOXX OOOOO OOOOOthe set of winning patterns (of which only one must be marked to have a bingo) is:
XXOXX XXOOO XXOOO OOOXX OOOXX OOOOO
For each data set, output a single line containing the fewest amount of numbers that still need to be called to form a bingo.
3 0 1 0 2 1 4 2 XXOOO OOOXX OOOOO OOOOO XXOOO OOOXX OOOOO OOOOO OOOOO OOOOO OOOOO OOOOO OOOOO OOOOO XXOOO OOOXX OOOOO OOOOO XXOOO OOOXX 1 1 0 1 1 5 1 XXXXX OOOOO OOOOO OOOOO OOOOO OOOOO XXXXX OOOOO OOOOO OOOOO OOOOO OOOOO XXXXX OOOOO OOOOO OOOOO OOOOO OOOOO XXXXX OOOOO OOOOO OOOOO OOOOO OOOOO XXXXX 15 15 15 15 4 1 1 XXXXX XXXXX XXXXX XXXXX XXXXX
4 0 1
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