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Stripes is a two player game. Necessary requisites are a board and rectangular stripes in three colours: red, green and blue. All the red stripes have dimensions , green - , and blue - , where , and are integers. Players have at their disposal an unlimited pool of stripes of each colour.
A game board is a rectangle of dimensions and consists of fields of size .
Players make their moves by turns. Move consists of laying a stripe of any colour on the board. There are the following rules in force:
The first player is this one, who makes the first move in the game. It is said, that the first player has a winning strategy, if independently of the moves of the second player he can always win.
Write a program which:
The first line of the standard input consists of three integers , and , , equal to the lengths of stripes, adequately: red, green and blue ones. Numbers in the line are separated by single spaces.
The second line of the standard input consists of one number , , which is equal to the number of different boards to consider. Lines from the 3-rd to the ()-th consists of one number , . Number in the ()-th line is the length of the -th board.
The standard output should contain lines. Only one number should be written in the -th line of the file:
For the input data:
1 5 1 3 1 5 6
the correct result is:
1 1 2
Task author: Adam Borowski.