Breaking the Wall Codeforces Solution | Codeforces Problem Solution 2022

Breaking the Wall Codeforces Solution | Codeforces Problem Solution 2022

E. Breaking the Wall

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

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$n$ sections, aligned in a row. The 𝑖$i$-th section initially has durability 𝑎𝑖$a_i$. If durability of some section becomes 0$0$ 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$2$ damage to the target section and 1$1$ damage to adjacent sections. In other words, if the onager shoots at the section 𝑥$x$, then the durability of the section 𝑥$x$ decreases by 2$2$, and the durability of the sections 𝑥−1$x-1$ and 𝑥+1$x+1$ (if they exist) decreases by 1$1$ each.

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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

The first line contains one integer 𝑛$n$ (2≤𝑛≤2⋅105$2\le n\le 2\cdot {10}^5$) — the number of sections.

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The second line contains the sequence of integers 𝑎1,𝑎2,…,𝑎𝑛$a_1,a_2,\dots ,a_n$ (1≤𝑎𝑖≤106$1\le a_i\le {10}^6$), where 𝑎𝑖$a_i$ is the initial durability of the 𝑖$i$-th section.

Output

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

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