You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in c++17.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```cpp
<your code here>
```

Execution time limit: 2.0 seconds
Memory limit: 256.0 MB

# Problem
Monocarp plays "Rage of Empires II: Definitive Edition" — a strategic computer game. Right now he's planning to attack his opponent in the game, but Monocarp's forces cannot enter the opponent's territory since the opponent has built a wall.

The wall consists of $$$n$$$ sections, aligned in a row. The $$$i$$$-th section initially has durability $$$a_i$$$. If durability of some section becomes $$$0$$$ or less, this section is considered broken.

To attack the opponent, Monocarp needs to break at least two sections of the wall (any two sections: possibly adjacent, possibly not). To do this, he plans to use an onager — a special siege weapon. The onager can be used to shoot any section of the wall; the shot deals $$$2$$$ damage to the target section and $$$1$$$ damage to adjacent sections. In other words, if the onager shoots at the section $$$x$$$, then the durability of the section $$$x$$$ decreases by $$$2$$$, and the durability of the sections $$$x - 1$$$ and $$$x + 1$$$ (if they exist) decreases by $$$1$$$ each.

Monocarp can shoot at any sections any number of times, he can even shoot at broken sections.

Monocarp wants to calculate the minimum number of onager shots needed to break at least two sections. Help him!

## Input Format
The first line contains one integer $$$n$$$ ($$$2 \le n \le 2 \cdot 10^5$$$) — the number of sections.

The second line contains the sequence of integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_i \le 10^6$$$), where $$$a_i$$$ is the initial durability of the $$$i$$$-th section.

## Output Format
Print one integer — the minimum number of onager shots needed to break at least two sections of the wall.

## Examples
```input
5
20 10 30 10 20
```
```output
10
```
-----
```input
3
1 8 1
```
```output
1
```
-----
```input
6
7 6 6 8 5 8
```
```output
4
```
-----
```input
6
14 3 8 10 15 4
```
```output
4
```
-----
```input
4
1 100 100 1
```
```output
2
```
-----
```input
3
40 10 10
```
```output
7
```

## Note
In the first example, it is possible to break the $$$2$$$-nd and the $$$4$$$-th section in $$$10$$$ shots, for example, by shooting the third section $$$10$$$ times. After that, the durabilities become $$$[20, 0, 10, 0, 20]$$$. Another way of doing it is firing $$$5$$$ shots at the $$$2$$$-nd section, and another $$$5$$$ shots at the $$$4$$$-th section. After that, the durabilities become $$$[15, 0, 20, 0, 15]$$$.

In the second example, it is enough to shoot the $$$2$$$-nd section once. Then the $$$1$$$-st and the $$$3$$$-rd section will be broken.

In the third example, it is enough to shoot the $$$2$$$-nd section twice (then the durabilities become $$$[5, 2, 4, 8, 5, 8]$$$), and then shoot the $$$3$$$-rd section twice (then the durabilities become $$$[5, 0, 0, 6, 5, 8]$$$). So, four shots are enough to break the $$$2$$$-nd and the $$$3$$$-rd section.

Now solve the problem and return the code.