Mr. Zavis bought a new garden. But it did not turn to yield a profit. Therefore he decided to take part in the Original Garden Contest. He hopes to win the contest and be awarded with a lot of money. Only square gardens can take part in this contest. The garden wins the contest if no other known square garden is similar to it. Mr. Zavis got hold of a list of all the known square gardens and started to compare.
Task: The input data consist of number N (size of the garden) and two matrixes of type NxN containing numbers 0 and 1 (0 denotes empty place, 1 denotes flowerbed). Write a program which determines whether these two gardens are similar. Two gardens are similar if one can be obtainted from the other using several operations of rotation by 90 degrees and symmetry about the x or y axis.
Example:
Input:
N = 4
1 0 0 0 0 0 1 0
0 0 1 1 1 0 1 0
0 1 0 0 0 1 0 0
0 0 1 0 0 0 0 1
Output:
Gardens are similar (the second can be obtained from the first one by turning
by 90 degrees right and using symmetry about the x-axis.
The princess of Tiribaki refused to marry the Burundi chieftain. It looked like another international conflict. But both sides were able to come to an agreement. They will play one match of their national game and the winner will decide. The rules of this game are simple. They will cut two necklaces belonging to a princess and they will arrange beads of each necklace to a separate pile. After this they will move alternatingly. Each player removes during one move several beads from one of the piles. The number of beads removed during one move should be at least 1 and cannot exceed given constant k. The game is over when all the beads are removed. There are free alternatives of the game. In the alternative A loses the player who removed odd number of beads during entire game. In the alternative B loses the player who removes the last bead. In the alternative C wins the player who removes the last bead. The alternative used in a match as well as the number k will be chosen by lot before the match.
Task: Write a program which for given game determines for which player the winning strategy exists. It means to decide which player can win regardless of the moves of his rival. Your program should be also able to advice to the winning player how to move if the player enters the moves of his rival. The input of your program consists of numbers N1 and N2 giving the numbers of beads in both piles, the number k and alternative H. The princess moves first.
Note: In the alternative A you can assume that the sum N1 + N2 is an odd number.
Lord Zoltan loves horse races. He also loves betting. Each Sunday he meets his friends at the horse races. Once they started to talk about their bets. "I betted two hundred gold coins that the Yellow Star will be better than Slyboot," said one of them . "And I betted barrel of my best wine that Artefax will be better than Halifax," said another lord. Lord Zoltan betted twenty-five silver coins that his favoured horse Iron will be better than Wooden Leg.
They discoverd that each of them did a bet of the type "the horse 1 will be better than the horse 2". After the races some of the friends went home happy, others (including Zoltan) tried not to show their sorrow. Going home Zoltan started to think. He wanted to know whether it was possible for all of them to win. Task: The input consist of the number of horses M, the number of bets N and N bets - bet "the horse A(i) will be better than the horse B(i)" will be given as the pair of numbers A(i), B(i). Write a program which finds one possible result of races (i.e. the order in which the horses finished) such that all the lords will win their bets. If no such result exists write appropriate message.
Example:
Input:
M=7, N=4
Bets:
1 2
2 3
3 4
3 1
Output:
No such result exist.
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Mohammed said: "When the clock starts to strike six o'clok wherever you are you should kneel down turning your faces towards holy places in Mekka and start to pray." And his followers spread to entire world and they did what Mohammed told them.
Once several Mohammedans met at one square at six o'clock. Nobody of them knew precisely where Mekka is. Each of them turns where he suppose Mekka to be. Then he wants to ensure himself that his direction is correct and he takes a look at the nearest Mohammedan sitting in front of him and he turns to the same direction as his fellow sits. All Mohammedans turn at the same time each second. Mohammedans who do not see any of their fellows in front of them and Mohammedans who look at the Mohammedan turned in the same direction as they are do not turn.
Task: The square is divided into MxN little squares. Each little sqaure can contain one of the following four objects: 'N','S','E','W' ('N' is a Mohammedan turned to the north,... 'W' is a Mohammedan turned to the west).
Example:
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