Problem:
Score : 600 points

Problem Statement

Given is an integer sequence A_1, ..., A_N of length N.

We will choose exactly \left\lfloor \frac{N}{2} \right\rfloor elements from this sequence so that no two adjacent elements are chosen.

Find the maximum possible sum of the chosen elements.

Here \lfloor x \rfloor denotes the greatest integer not greater than x.

Constraints

2 \leq N \leq 2\times 10^5

|A_i|\leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 ... A_N

Output

Print the maximum possible sum of the chosen elements.

Sample Input 1

6
1 2 3 4 5 6

Sample Output 1

12

Choosing 2, 4, and 6 makes the sum 12, which is the maximum possible value.

Sample Input 2

5
-1000 -100 -10 0 10

Sample Output 2

0

Choosing -10 and 10 makes the sum 0, which is the maximum possible value.

Sample Input 3

10
1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000

Sample Output 3

5000000000

Watch out for overflow.

Sample Input 4

27
18 -28 18 28 -45 90 -45 23 -53 60 28 -74 -71 35 -26 -62 49 -77 57 24 -70 -93 69 -99 59 57 -49

Sample Output 4

295

Solution in Rust (1.42.0) (judge verdict: Accepted)

#[macro_use]
mod input_mcr {
    // ref: tanakh <https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8>
    // diff: using Parser
    #[macro_export(local_inner_macros)]
    macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut parser = Parser::from_str($s);
        input_inner!{parser, $($r)*}
    };
    (parser = $parser:ident, $($r:tt)*) => {
        input_inner!{$parser, $($r)*}
    };
    (new_stdin_parser = $parser:ident, $($r:tt)*) => {
        let stdin = std::io::stdin();
        let reader = std::io::BufReader::new(stdin.lock());
        let mut $parser = Parser::new(reader);
        input_inner!{$parser, $($r)*}
    };
    ($($r:tt)*) => {
        input!{new_stdin_parser = parser, $($r)*}
    };
}

    #[macro_export(local_inner_macros)]
    macro_rules! input_inner {
    ($parser:ident) => {};
    ($parser:ident, ) => {};
    ($parser:ident, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($parser, $t);
        input_inner!{$parser $($r)*}
    };
}

    #[macro_export(local_inner_macros)]
    macro_rules! read_value {
    ($parser:ident, ( $($t:tt),* )) => {
        ( $(read_value!($parser, $t)),* )
    };
    ($parser:ident, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($parser, $t)).collect::<Vec<_>>()
    };
    ($parser:ident, chars) => {
        read_value!($parser, String).chars().collect::<Vec<char>>()
    };
    ($parser:ident, char_) => {
        read_value!($parser, String).chars().collect::<Vec<char>>()[0]
    };
    ($parser:ident, usize1) => {
        read_value!($parser, usize) - 1
    };
    ($parser:ident, line) => {
        $parser.next_line()
    };
    ($parser:ident, line_) => {
        $parser.next_line().chars().collect::<Vec<char>>()
    };
    ($parser:ident, i64_) => {
        $parser.fast_i64()
    };
    ($parser:ident, usize_) => {
        $parser.fast_i64() as usize
    };
    ($parser:ident, usize1_) => {
        ($parser.fast_i64() - 1) as usize
    };
    ($parser:ident, $t:ty) => {
        $parser.next::<$t>().expect("Parse error")
    };
}

    use std::io;
    use std::io::BufRead;
    use std::str;

    // ref: tatsuya6502 <https://qiita.com/tatsuya6502/items/cd448486f7ef7b5b8c7e>
    // ref: wariuni <https://qiita.com/tatsuya6502/items/cd448486f7ef7b5b8c7e#comment-7040a5ae96305e884eb9>
    // diff: using std::io::BufRead::fill_buf()
    pub struct Parser<R> {
        pub reader: R,
        buf: Vec<u8>,
        pos: usize,
    }

    impl Parser<io::Empty> {
        pub fn from_str(s: &str) -> Parser<io::Empty> {
            Parser {
                reader: io::empty(),
                buf: s.as_bytes().to_vec(),
                pos: 0,
            }
        }
    }

    impl<R: BufRead> Parser<R> {
        pub fn new(reader: R) -> Parser<R> {
            Parser {
                reader: reader,
                buf: vec![],
                pos: 0,
            }
        }
        pub fn update_buf(&mut self) {
            self.buf.clear();
            self.pos = 0;
            loop {
                let (len, complete) = {
                    let buf2 = self.reader.fill_buf().unwrap();
                    self.buf.extend_from_slice(buf2);
                    let len = buf2.len();
                    (len, buf2[len - 1] <= 0x20)
                };
                self.reader.consume(len);
                if complete {
                    break;
                }
            }
        }
        pub fn next<T: str::FromStr>(&mut self) -> Result<T, T::Err> {
            loop {
                let mut begin = self.pos;
                while begin < self.buf.len() && (self.buf[begin] <= 0x20) {
                    begin += 1;
                }
                let mut end = begin;
                while end < self.buf.len() && (self.buf[end] > 0x20) {
                    end += 1;
                }
                if begin != self.buf.len() {
                    self.pos = end;
                    return unsafe { str::from_utf8_unchecked(&self.buf[begin..end]) }.parse::<T>();
                } else {
                    self.update_buf();
                }
            }
        }
        pub fn next_line(&mut self) -> String {
            loop {
                let mut begin = self.pos;
                if begin < self.buf.len() && (self.buf[begin] < 0x20) {
                    begin += 1;
                }
                let mut end = begin;
                while end < self.buf.len() && (self.buf[end] >= 0x20) {
                    end += 1;
                }
                if begin != self.buf.len() {
                    self.pos = end;
                    return unsafe { str::from_utf8_unchecked(&self.buf[begin..end]) }.to_string();
                } else {
                    self.update_buf();
                }
            }
        }
        pub fn fast_i64(&mut self) -> i64 {
            loop {
                let mut begin = self.pos;
                while begin < self.buf.len() && (self.buf[begin] <= 0x20) {
                    begin += 1;
                }
                if begin == self.buf.len() {
                    self.update_buf();
                    continue;
                }
                let mut res = 0;
                let (is_positive, mut end) = match self.buf[begin] {
                    b'+' => (true, begin + 1),
                    b'-' => (false, begin + 1),
                    _ => (true, begin),
                };
                while end < self.buf.len() && (self.buf[end] > 0x20) {
                    res = res * 10 + (self.buf[end] as i64 - '0' as i64);
                    end += 1;
                }
                if begin != self.buf.len() {
                    self.pos = end;
                    return if is_positive { res } else { -res };
                } else {
                    self.update_buf();
                }
            }
        }
    }
}

mod cumulative {
    use std::ops::*;

    pub fn cu<T: Add<Output = T> + Copy>(zero: T, xs: &Vec<T>) -> Vec<T> {
        let mut res = vec![zero; xs.len() + 1];
        for (i, &x) in xs.iter().enumerate() {
            res[i + 1] = res[i] + x;
        }
        res
    }
}

use input_mcr::*;
use std::cmp::*;

use cumulative::*;

fn main() {
    input! {
        n: usize,
        xs: [i64; n],
    }
    let mut yss = vec![vec![0; n]; 2];
    for i in 0..n {
        yss[i % 2][i] = xs[i];
    }
    let zss = vec![cu(0, &yss[0]), cu(0, &yss[1])];
    // eprintln!("zss[0] = {:?}", zss[0]);
    // eprintln!("zss[1] = {:?}", zss[1]);
    let inf = 1i64 << 60;
    let mut res = -inf;
    if n % 2 == 0 {
        res = max(res, zss[0][n - 1]);
        res = max(res, zss[1][n] - zss[1][1]);
        let mut i = 1;
        while i + 2 < n {
            let t = zss[0][i] + (zss[1][n] - zss[1][i + 2]);
            // eprintln!("t = {:?}", t);
            res = max(res, t);
            i = i + 2;
        }
    } else {
        res = max(res, zss[0][n - 2]); // 0(1)
        res = max(res, zss[0][n] - zss[0][2]);
        res = max(res, zss[1][n - 1]);
        res = max(res, zss[1][n] - zss[1][1]); // extra
        let mut i = 1;
        while i + 2 <= n {
            let t = zss[0][i] + (zss[1][n] - zss[1][i + 2]);
            // eprintln!("t = {:?}, even: {}, odd: {}", t, i, i+2);
            res = max(res, t);
            i = i + 2;
        }
        let mut i = 0;
        while i + 2 <= n {
            let t = zss[1][i] + (zss[0][n] - zss[0][i + 2]);
            // eprintln!("t = {:?}, odd: {}, even: {}", t, i, i+2);
            res = max(res, t);
            i = i + 2;
        }
        let mut i = 1;
        while i + 3 <= n {
            let t = zss[0][i] + (zss[0][n] - zss[0][i + 3]);
            // eprintln!("t = {:?}, even: {}, even: {}", t, i, i+3);
            res = max(res, t);
            i = i + 2;
        }
        let mut dp = vec![-inf; n];
        dp[0] = xs[0];
        dp[1] = xs[1];
        for i in 2..n {
            if i % 2 == 0 {
                dp[i] = dp[i - 2] + xs[i];
            } else {
                dp[i] = max(dp[i], dp[i - 2] + xs[i]);
                dp[i] = max(dp[i], dp[i - 3] + xs[i]);
            }
        }
        let mut i = 1;
        while i + 3 <= n {
            let t = dp[i] + (zss[0][n] - zss[0][i + 3]);
            res = max(res, t);
            i = i + 2;
        }
    }
    println!("{}", res);
}