The Utopian Tree goes through 2 cycles of growth every year. Each spring, it doubles in height. Each summer, its height increases by 1 meter.
A Utopian Tree sapling with a height of 1 meter is planted at the onset of spring. How tall will the tree be after growth cycles?
For example, if the number of growth cycles is n = 5, the calculations are as follows:
Period Height
0 1
1 2
2 3
3 6
4 7
5 14
[in]
0
1
4
[out]
1
2
7
There are 3 test cases.
In the first case (n = 0), the initial height (1) of the tree remains unchanged.
In the second case (n = 1), the tree doubles in height and is 2 meters tall after the spring cycle.
In the third case (n = 4), the tree doubles its height in spring (n = 1, height = 2), then grows a meter in summer (n = 2, height = 3), then doubles after the next spring (n = 3, height = 6), and grows another meter after summer (n = 4, height = 7). Thus, at the end of 4 cycles, its height is 7 meters.