CF305C Ivan and Powers of Two

Ivan has got an array of $ n $ non-negative integers $ a_{1},a_{2},...,a_{n} $ . Ivan knows that the array is sorted in the non-decreasing order. Ivan wrote out integers $ 2^{a_{1}},2^{a_{2}},...,2^{a_{n}} $ on a piece of paper. Now he wonders, what minimum number of integers of form $ 2^{b} $ $ (b>=0) $ need to be added to the piece of paper so that the sum of all integers written on the paper equalled $ 2^{v}-1 $ for some integer $ v $ $ (v>=0) $ . Help Ivan, find the required quantity of numbers.

The first line contains integer $ n $ ( $ 1

Print a single integer — the answer to the problem.

In the first sample you do not need to add anything, the sum of numbers already equals $ 2^{3}-1=7 $ . In the second sample you need to add numbers $ 2^{0},2^{1},2^{2} $ .