B"Gildong is developing a game consisting of n stages numbered from 1 to n . The player starts the game from the 1 -st stage and should beat the stages in increasing order of the stage number. The player wins the game after beating the n -th stage. There is at most one checkpoint on each stage, and there is always a checkpoint on the 1 -st stage. At the beginning of the game, only the checkpoint on the 1 -st stage is activated, and all other checkpoints are deactivated. When the player gets to the i -th stage that has a checkpoint, that checkpoint is activated. For each try of a stage, the player can either beat the stage or fail the stage. If they beat the i -th stage, the player is moved to the i+1 -st stage. If they fail the i -th stage, the player is moved to the most recent checkpoint they activated, and they have to beat the stages after that checkpoint again. For example, assume that n = 4 and the checkpoints are on the 1 -st and 3 -rd stages. The player starts at the 1 -st stage. If they fail on the 1 -st stage, they need to retry the 1 -st stage because the checkpoint on the 1 -st stage is the most recent checkpoint they activated. If the player beats the 1 -st stage, they're moved to the 2 -nd stage. If they fail it, they're sent back to the 1 -st stage again. If they beat both the 1 -st stage and the 2 -nd stage, they get to the 3 -rd stage and the checkpoint on the 3 -rd stage is activated. Now whenever they fail on the 3 -rd stage, or the 4 -th stage after beating the 3 -rd stage, they're sent back to the 3 -rd stage. If they beat both the 3 -rd stage and the 4 -th stage, they win the game. Gildong is going to build the stages to have equal difficulty. He wants you to find any series of stages and checkpoints using at most 2000 stages, where the expected number of tries over all stage"...