CF863G Graphic Settings

Recently Ivan bought a new computer. Excited, he unpacked it and installed his favourite game. With his old computer Ivan had to choose the worst possible graphic settings (because otherwise the framerate would be really low), but now he wants to check, maybe his new computer can perform well even with the best possible graphics? There are $ m $ graphics parameters in the game. $ i $ -th parameter can be set to any positive integer from $ 1 $ to $ a_{i} $ , and initially is set to $ b_{i} $ ( $ b_{i}

The first line of input contains one integer number $ m $ ( $ 1

If there is a way to make exactly $ p $ changes (each change either decreases or increases some parameter by $ 1 $ ) to try all possible combinations and return to initial combination, then output Cycle in the first line. Then $ p $ lines must follow, each desribing a change. The line must be either inc x (increase parameter $ x $ by $ 1 $ ) or dec x (decrease it). Otherwise, if there is a way to make exactly $ p-1 $ changes to try all possible combinations (including the initial one), then output Path in the first line. Then $ p-1 $ lines must follow, each describing the change the same way as mentioned above. Otherwise, output No.