Statement

William is playing the Wheel of Fortune, a famous game show. The wheel is a "sliced" circle, with numbers on each slice. It can be seen as a circular array of 2N elements. The rules are as follows. William can "turn" the wheel by rotating the array, i.e. moving each of its elements ahead by some positions (possibly making several complete turns). For example, if the array is 2 1 5 3, a rotation of 1 would yield the following array: 3 2 1 5. Rotating again by 2 would yield 1 5 3 2. Rotating again by 1 would yield the original array. In order to win the game, William needs some information about the wheel everytime he turns it. Specifically: he needs to know the min among the first N elements and the max among the last N elements. Initially, in the previous example, the min and max values are 1 and 5. After the first rotation they become 2 and 5, then they become 1 and 3, and finally they become 1 and 5 again when the original ordering is restored...