Convex Sequence

An integer sequence $x_0, x_1, \dots, x_{N-1}$ is convex when $x_{i-1} + x_{i+1} \ge 2 x_i$ holds for every $i$ with $1 \le i \le N-2$. A sequence of length 1 or 2 is always convex.

For example, 7, 3, 4, 5, 7 and 4, 2, 1, 3 are convex, while 4, 3, 1, 2 and 5, 7, 3 are not.

You are given a sequence $A = a_0, a_1, \dots, a_{N-1}$. One operation picks an index $i$ and replaces $a_i$ with $a_i - 1$, and no other operation is allowed. You may pick the same index several times, and an element may become negative. Write a program that finds the minimum number of operations that makes $A$ convex.

The first line contains the size of the sequence, $N$ ($1 \le N \le 50$). The second line contains the integers $a_0, a_1, \dots, a_{N-1}$ ($0 \le a_i \le 10^9$) of the sequence $A$, separated by spaces.

Print the minimum number of operations that makes $A$ convex on the first line.