Problem:
Score: 200 points

Problem Statement

Takahashi, who works at DISCO, is standing before an iron bar.
The bar has N-1 notches, which divide the bar into N sections. The i-th section from the left has a length of A_i millimeters.

Takahashi wanted to choose a notch and cut the bar at that point into two parts with the same length.
However, this may not be possible as is, so he will do the following operations some number of times before he does the cut:

Choose one section and expand it, increasing its length by 1 millimeter. Doing this operation once costs 1 yen (the currency of Japan).

Choose one section of length at least 2 millimeters and shrink it, decreasing its length by 1 millimeter. Doing this operation once costs 1 yen.

Find the minimum amount of money needed before cutting the bar into two parts with the same length.

Constraints

2 \leq N \leq 200000

1 \leq A_i \leq 2020202020

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 A_3 ... A_N

Output

Print an integer representing the minimum amount of money needed before cutting the bar into two parts with the same length.

Sample Input 1

3
2 4 3

Sample Output 1

3

The initial lengths of the sections are [2, 4, 3] (in millimeters). Takahashi can cut the bar equally after doing the following operations for 3 yen:

Shrink the second section from the left. The lengths of the sections are now [2, 3, 3].

Shrink the first section from the left. The lengths of the sections are now [1, 3, 3].

Shrink the second section from the left. The lengths of the sections are now [1, 2, 3], and we can cut the bar at the second notch from the left into two parts of length 3 each.

Sample Input 2

12
100 104 102 105 103 103 101 105 104 102 104 101

Sample Output 2

0

Solution in Rust (1.15.1) (judge verdict: Accepted)

use std::cmp::*;
use std::collections::*;
use std::io::*;
use std::str::*;
use std::string::*;
use std::f64::consts::PI;

macro_rules! read {
    (($($t:tt),*)) => {
        ( $(read!($t)),* )
    };
    ([[$t:tt; $len1:expr]; $len2:expr]) => {
        (0..$len2).map(|_| read!([$t; $len1])).collect::<Vec<_>>()
    };

    ([$t:tt; $len:expr]) => {
        (0..$len).map(|_| read!($t)).collect::<Vec<_>>()
    };

    (chars) => {
        read!(String).chars().collect::<Vec<char>>()
    };

    (usize1) => {
        read!(usize) - 1
    };

    ($t:ty) => {{
        let stdin = stdin();
        let stdin = stdin.lock();
        let token: String = stdin
            .bytes()
            .map(|c| c.unwrap() as char)
            .skip_while(|c| c.is_whitespace())
            .take_while(|c| !c.is_whitespace())
            .collect();

        token.parse::<$t>().unwrap()
    }};
}

macro_rules! input {
    (mut $name:ident: $t:tt, $($r:tt)*) => {
        let mut $name = read!($t);
        input!($($r)*);
    };

    (mut $name:ident: $t:tt) => {
        let mut $name = read!($t);
    };

    ($name:ident: $t:tt, $($r:tt)*) => {
        let $name = read!($t);
        input!($($r)*);
    };

    ($name:ident: $t:tt) => {
        let $name = read!($t);
    };
}

macro_rules! min {
    ($a:expr $(,)*) => {{
        $a
    }};
    ($a:expr, $b:expr $(,)*) => {{
        std::cmp::min($a, $b)
    }};
    ($a:expr, $($rest:expr),+ $(,)*) => {{
        std::cmp::min($a, min!($($rest),+))
    }};
}

macro_rules! chmin {
    ($base:expr, $($cmps:expr),+ $(,)*) => {{
        let cmp_min = min!($($cmps),+);
        if $base > cmp_min {
            $base = cmp_min;
            true
        } else {
            false
        }
    }};
}

macro_rules! max {
    ($a:expr $(,)*) => {{
        $a
    }};
    ($a:expr, $b:expr $(,)*) => {{
        std::cmp::max($a, $b)
    }};
    ($a:expr, $($rest:expr),+ $(,)*) => {{
        std::cmp::max($a, max!($($rest),+))
    }};
}

macro_rules! chmax {
    ($base:expr, $($cmps:expr),+ $(,)*) => {{
        let cmp_max = max!($($cmps),+);
        if $base < cmp_max {
            $base = cmp_max;
            true
        } else {
            false
        }
    }};
}

#[derive(Eq, PartialEq, Clone, Debug)]
pub struct Rev<T>(pub T);

impl<T: PartialOrd> PartialOrd for Rev<T> {
    fn partial_cmp(&self, other: &Rev<T>) -> Option<std::cmp::Ordering> {
        other.0.partial_cmp(&self.0)
    }
}

impl<T: Ord> Ord for Rev<T> {
    fn cmp(&self, other: &Rev<T>) -> std::cmp::Ordering {
        other.0.cmp(&self.0)
    }
}

struct IO<R, W: std::io::Write>(R, std::io::BufWriter<W>);

impl<R: std::io::Read, W: std::io::Write> IO<R, W> {
    pub fn new(r: R, w: W) -> Self {
        IO(r, std::io::BufWriter::new(w))
    }

    pub fn write<S: ToString>(&mut self, s: S) {
        use std::io::Write;
        self.1.write(s.to_string().as_bytes()).unwrap();
    }

    pub fn read<T: std::str::FromStr>(&mut self) -> T {
        use std::io::Read;
        let s: String = self
            .0
            .by_ref()
            .bytes()
            .map(|b| b.unwrap() as char)
            .skip_while(|c| c.is_whitespace())
            .take_while(|c| !c.is_whitespace())
            .collect();

        return s.parse::<T>().ok().unwrap();
    }

    pub fn vec<T: std::str::FromStr>(&mut self, n: usize) -> Vec<T> {
        (0..n).map(|_| self.read()).collect()
    }

    pub fn chars(&mut self) -> Vec<char> {
        self.read::<String>().chars().collect()
    }
}

fn prime_factorization(n: i64) -> HashMap<i64, i64> {
    let mut n = n;
    let mut res = HashMap::new();
    let mut i = 2;
    while i * i <= n {
        while n % i == 0 {
            n /= i;
            let count = res.entry(i).or_insert(0);
            *count += 1;
        }
        i += 1;
    }

    if n > 1 {
        res.insert(n, 1);
    }

    return res;
}

//
// struct Combination {
//     MOD: i64,
//     fac: Vec<i64>,
//     fac_inv: Vec<i64>,
// }
//
// impl Combination {
//     pub fn new(n: i64) -> Self {
//         let MOD: i64 = 1_000_000_007;
//         let mut fac: Vec<i64> = vec![0; n as usize + 1];
//         let mut fac_inv: Vec<i64> = vec![0; n as usize + 1];
//
//         let get_inverse = |mut n: i64| -> i64 {
//             let (mut res, mut p) = (1, MOD - 2);
//
//             while p != 0 {
//                 if p & 1 == 1 {
//                     res = (res * n) % MOD;
//                 }
//                 n = (n * n) % MOD;
//                 p >>= 1;
//             }
//
//             return res;
//         };
//
//         fac[0] = 1;
//
//         for i in 1..n + 1 {
//             fac[i as usize] = (fac[i as usize - 1] * i) % MOD;
//         }
//
//         for i in 0..n + 1 {
//             fac_inv[i as usize] = get_inverse(fac[i as usize]);
//         }
//
//         Combination {
//             MOD: MOD,
//             fac: fac,
//             fac_inv: fac_inv,
//         }
//     }
//
//     fn nCr(&self, n: i64, r: i64) -> i64 {
//         if n < r {
//             return 0;
//         }
//
//         let a: i64 = self.fac[n as usize];
//         let b: i64 = self.fac_inv[(n - r) as usize];
//         let c: i64 = self.fac_inv[r as usize];
//         let bc: i64 = (b * c) % self.MOD;
//
//         return (a * bc) % self.MOD;
//     }
//
//     fn nPr(&self, n: i64, r: i64) -> i64 {
//         if n < r {
//             return 0;
//         }
//
//         let a: i64 = self.fac[n as usize];
//         let b: i64 = self.fac_inv[(n - r) as usize];
//
//         return (a * b) % self.MOD;
//     }
//
//     fn nHr(&self, n: i64, r: i64) -> i64 {
//         if n == 0 && r == 0 {
//             return 1;
//         }
//
//         return self.nCr(n + r - 1, r);
//     }
// }


#[derive(Copy, Clone, Eq, PartialEq)]
struct Edge {
    to: usize,
    cost: i64,
}

fn dijkstra(graph: &Vec<Vec<Edge>>, s: &usize) -> Vec<i64> {
    use std::collections::BinaryHeap;
    let mut dist = vec![1e18 as i64; graph.len()];
    let mut heap = BinaryHeap::new();
    dist[*s] = 0;
    heap.push(Rev((0, *s)));
    while let Some(Rev((cost, v))) = heap.pop() {
        if dist[v] < cost {
            continue;
        }

        for e in &graph[v] {
            if dist[e.to] <= dist[v] + e.cost {
                continue;
            }
            dist[e.to] = dist[v] + e.cost;
            heap.push(Rev((dist[e.to], e.to)));
        }
    }
    return dist;
}

struct LCA {
    par: Vec<Vec<Option<usize>>>,
    dist: Vec<i64>,
}

impl LCA {
    pub fn new(graph: &Vec<Vec<usize>>, root: &usize) -> LCA {
        let V = graph.len();
        let mut K = 1;

        while (1 << K) < V {
            K += 1;
        }

        let mut par = vec![vec![None; V]; K];
        let mut dist = vec![-1; V];
        let graph = graph.to_vec();

        fn dfs(
            v: usize,
            p: Option<usize>,
            d: i64,
            graph: &Vec<Vec<usize>>,
            par: &mut Vec<Vec<Option<usize>>>,
            dist: &mut Vec<i64>,
        ) {
            par[0][v] = p;
            dist[v] = d;
            for &to in &graph[v] {
                match p {
                    Some(p) => {
                        if to != p {
                            dfs(to, Some(v), d + 1, graph, par, dist)
                        }
                    }
                    None => dfs(to, Some(v), d + 1, graph, par, dist),
                }
            }
        }

        dfs(*root, None, 0, &graph, &mut par, &mut dist);

        for k in 0..K - 1 {
            for v in 0..V {
                match par[k][v] {
                    Some(x) => par[k + 1][v] = par[k][x],
                    None => (),
                }
            }
        }

        LCA {
            par: par,
            dist: dist,
        }
    }

    pub fn query(&self, u: usize, v: usize) -> usize {
        let mut u = u;
        let mut v = v;
        if self.dist[u] < self.dist[v] {
            return self.query(v, u);
        }

        let K = self.par.len();
        for k in 0..K {
            if ((self.dist[u] - self.dist[v]) >> k & 1) == 1 {
                u = self.par[k][u].unwrap();
            }
        }

        if u == v {
            return u;
        }

        for k in (0..K - 1).rev() {
            if self.par[k][u] != self.par[k][v] {
                u = self.par[k][u].unwrap();
                v = self.par[k][v].unwrap();
            }
        }

        return self.par[0][u].unwrap();
    }
}

struct Doubling {
    N: usize,
    LOG: usize,
    next: Vec<Vec<Option<usize>>>,
}

impl Doubling {
    pub fn new(vec: &Vec<usize>, lim: &usize) -> Doubling {
        let N = vec.len();
        let lim = *lim;
        let mut LOG = 1;
        while (1 << LOG) < 2 * lim {
            LOG += 1;
        }

        let mut next = vec![vec![None; N]; LOG];

        for i in 0..N {
            next[0][i] = Some(vec[i]);
        }

        for k in 0..LOG - 1 {
            for i in 0..N {
                match next[k][i] {
                    Some(x) => next[k + 1][i] = next[k][x],
                    None => (),
                }
            }
        }

        Doubling {
            N: N,
            LOG: LOG,
            next: next,
        }
    }

    pub fn query(&self, i: usize, n: usize) -> usize {
        let mut i = i;
        for k in (0..self.LOG).rev() {
            if (n >> k) & 1 == 1 {
                i = self.next[k][i].unwrap();
            }
        }
        return i;
    }
}


struct UnionFind {
    par: Vec<i32>,
}

impl UnionFind {
    pub fn new(n: usize) -> UnionFind {
        UnionFind {
            par: vec![-1; n],
        }
    }

    pub fn root(&mut self, x: usize) -> usize {
        if self.par[x] < 0 {
            return x;
        } else {
            let a = self.par[x] as usize;
            self.par[x] = self.root(a) as i32;
            return self.par[x] as usize;
        }
    }

    pub fn is_same(&mut self, x: usize, y: usize) -> bool {
        self.root(x) == self.root(y)
    }

    pub fn merge(&mut self, x: usize, y: usize) -> bool {
        let mut x = self.root(x);
        let mut y = self.root(y);
        if x == y {
            return false;
        } else {
            if self.par[x] > self.par[y] {
                std::mem::swap(&mut x, &mut y);
            }
            self.par[x] += self.par[y];
            self.par[y] = x as i32;
            return true;
        }
    }

    pub fn size(&mut self, x: usize) -> i64 {
        let a = self.root(x);
        return -self.par[a] as i64;
    }
}

trait Monoid {
    fn id() -> Self;
    fn op(&self, rhs: &Self) -> Self;
}

#[derive(Clone, Debug)]
struct Min(i64);

#[derive(Clone, Debug)]
struct RangeUpdate(i64);

#[derive(Clone, Debug)]
struct RangeAdd(i64);

#[derive(Clone, Debug)]
struct Sum(i64);

impl Monoid for Sum {
    fn id() -> Self {
        Sum(0)
    }

    fn op(&self, rhs: &Self) -> Self {
        Sum(self.0 + rhs.0)
    }
}

impl Monoid for Min {
    fn id() -> Self {
        Min(std::i32::MAX as i64)
    }

    fn op(&self, rhs: &Self) -> Self {
        Min(std::cmp::min(self.0, (*rhs).0))
    }
}

trait Operator {
    type T;
    fn id() -> Self;
    fn op(&self, rhs: &Self) -> Self;
    fn act(&self, tar: &Self::T, x: usize) -> Self::T;
}

impl Operator for RangeUpdate {
    type T = Min;
    fn id() -> Self {
        RangeUpdate(0)
    }

    fn op(&self, rhs: &Self) -> Self {
        (*rhs).clone()
    }

    fn act(&self, tar: &Self::T, x: usize) -> Self::T {
        Min(self.0)
    }
}

impl Operator for RangeAdd {
    type T = Sum;
    fn id() -> Self {
        RangeAdd(0)
    }

    fn op(&self, rhs: &Self) -> Self {
        RangeAdd(self.0 + rhs.0)
    }

    // Sum(tar.0 + self.0 * x as i64)
    fn act(&self, tar: &Self::T, x: usize) -> Self::T {
        Sum(tar.0 + self.0 * x as i64)
    }
}

struct LazySegTree<M: Monoid, O: Operator<T=M>> {
    dat: Vec<M>,
    lzy: Vec<O>,
    need_update: Vec<bool>,
    size: usize,
}

impl<M: Monoid + Clone, O: Operator<T=M> + Clone> LazySegTree<M, O> {
    pub fn new(vec: Vec<M>) -> LazySegTree<M, O> {
        let n = vec.len();
        let mut sz = 1;
        while sz < n {
            sz <<= 1;
        }
        let mut dat = vec![M::id(); sz << 1];
        for i in 0..n {
            dat[i + sz] = vec[i].clone();
        }
        for k in (1..sz).rev() {
            dat[k] = dat[k << 1].op(&dat[(k << 1) + 1]);
        }

        return LazySegTree {
            dat: dat,
            lzy: vec![O::id(); sz << 1],
            need_update: vec![false; sz << 1],
            size: sz,
        };
    }

    pub fn eval(&mut self, l: usize, r: usize, k: usize) {
        if !self.need_update[k] {
            return;
        }
        self.dat[k] = self.lzy[k].act(&self.dat[k], r - l);
        if (k << 1) < self.dat.len() {
            self.lzy[k << 1] = self.lzy[k << 1].op(&self.lzy[k]);
            self.lzy[(k << 1) + 1] = self.lzy[(k << 1) + 1].op(&self.lzy[k]);
            self.need_update[k << 1] = true;
            self.need_update[(k << 1) + 1] = true;
        }
        self.lzy[k] = O::id();
        self.need_update[k] = false;
    }

    pub fn update(&mut self, a: usize, b: usize, x: O) {
        let sz = self.size;
        self._update(a, b, &x, 0, sz, 1);
    }

    pub fn _update(&mut self, a: usize, b: usize, x: &O, l: usize, r: usize, k: usize) {
        self.eval(l, r, k);
        if b <= l || r <= a {
            return;
        } else if a <= l && r <= b {
            self.lzy[k] = self.lzy[k].op(x);
            self.need_update[k] = true;
            self.eval(l, r, k);
        } else {
            let mid = (l + r) >> 1;
            self._update(a, b, x, l, mid, k << 1);
            self._update(a, b, x, mid, r, (k << 1) + 1);
            self.dat[k] = self.dat[k << 1].op(&self.dat[(k << 1) + 1]);
        }
    }

    pub fn query(&mut self, a: usize, b: usize) -> M {
        let sz = self.size;
        return self._query(a, b, 0, sz, 1);
    }

    pub fn _query(&mut self, a: usize, b: usize, l: usize, r: usize, k: usize) -> M {
        self.eval(l, r, k);
        if b <= l || r <= a {
            return M::id();
        } else if a <= l && r <= b {
            return self.dat[k].clone();
        } else {
            let mid = (l + r) >> 1;
            let vl = self._query(a, b, l, mid, k << 1);
            let vr = self._query(a, b, mid, r, (k << 1) + 1);
            return vl.op(&vr);
        }
    }
}

struct SegTree<M: Monoid> {
    dat: Vec<M>,
    size: usize,
}

impl<M: Monoid + Clone> SegTree<M> {
    pub fn new(n: usize) -> SegTree<M> {
        let mut sz = 1;
        while sz < n {
            sz <<= 1;
        }

        SegTree::<M> {
            dat: vec![M::id(); sz * 2],
            size: sz,
        }
    }

    pub fn update(&mut self, k: usize, val: M) {
        let mut k = k + self.size;
        self.dat[k] = val;
        while k > 0 {
            k = k >> 1;
            self.dat[k] = self.dat[k << 1].op(&self.dat[(k << 1) + 1]);
        }
    }

    pub fn query(&self, a: usize, b: usize) -> M {
        let mut lx = M::id();
        let mut rx = M::id();
        let mut l = a + self.size;
        let mut r = b + self.size;
        while l < r {
            if (l & 1) == 1 {
                lx = lx.op(&self.dat[l]);
                l += 1;
            }

            if (r & 1) == 1 {
                r -= 1;
                rx = self.dat[r].op(&rx);
            }

            l >>= 1;
            r >>= 1;
        }

        return lx.op(&rx);
    }
}

fn decode(v: Vec<char>) -> Vec<(char, usize)> {
    let mut res = Vec::new();
    let mut now = v[0];
    let mut cnt = 1;

    for i in 1..v.len() {
        if v[i] == now {
            cnt += 1;
        } else {
            res.push((now, cnt));
            cnt = 1;
            now = v[i];
        }
    }
    res.push((now, cnt));

    return res;
}


use std::ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Sub, SubAssign};

type Num = usize;

#[derive(Clone, Copy)]
pub struct ModInt<T: Copy + Clone>(pub T);

impl Add<ModInt<Num>> for ModInt<Num> {
    type Output = ModInt<Num>;
    fn add(self, rhs: ModInt<Num>) -> ModInt<Num> {
        self + rhs.0
    }
}

impl Add<Num> for ModInt<Num> {
    type Output = ModInt<Num>;
    fn add(self, mut rhs: Num) -> ModInt<Num> {
        if rhs >= MOD {
            rhs %= MOD;
        }
        let mut t = rhs + self.0;
        if t >= MOD {
            t = t - MOD;
        }
        ModInt(t)
    }
}

impl Sub<Num> for ModInt<Num> {
    type Output = ModInt<Num>;
    fn sub(self, rhs: Num) -> ModInt<Num> {
        let rhs = if rhs >= MOD { rhs % MOD } else { rhs };
        let value = if self.0 < rhs { self.0 + MOD } else { self.0 };
        ModInt(value - rhs)
    }
}

impl Sub<ModInt<Num>> for ModInt<Num> {
    type Output = ModInt<Num>;
    fn sub(self, rhs: ModInt<Num>) -> ModInt<Num> {
        self - rhs.0
    }
}

impl AddAssign<Num> for ModInt<Num> {
    fn add_assign(&mut self, other: Num) {
        *self = *self + other;
    }
}

impl AddAssign<ModInt<Num>> for ModInt<Num> {
    fn add_assign(&mut self, other: ModInt<Num>) {
        *self = *self + other;
    }
}

impl SubAssign<Num> for ModInt<Num> {
    fn sub_assign(&mut self, other: Num) {
        *self = *self - other;
    }
}

impl SubAssign<ModInt<Num>> for ModInt<Num> {
    fn sub_assign(&mut self, other: ModInt<Num>) {
        *self = *self - other;
    }
}

impl Div<Num> for ModInt<Num> {
    type Output = ModInt<Num>;
    fn div(self, mut rhs: Num) -> ModInt<Num> {
        if rhs >= MOD {
            rhs %= MOD;
        }
        self * ModInt(rhs).pow(MOD - 2)
    }
}

impl Div<ModInt<Num>> for ModInt<Num> {
    type Output = ModInt<Num>;
    fn div(self, rhs: ModInt<Num>) -> ModInt<Num> {
        self / rhs.0
    }
}

impl DivAssign<Num> for ModInt<Num> {
    fn div_assign(&mut self, rhs: Num) {
        *self = *self / rhs
    }
}

impl DivAssign<ModInt<Num>> for ModInt<Num> {
    fn div_assign(&mut self, rhs: ModInt<Num>) {
        *self = *self / rhs
    }
}

impl Mul<ModInt<Num>> for ModInt<Num> {
    type Output = ModInt<Num>;

    fn mul(self, rhs: ModInt<Num>) -> ModInt<Num> {
        self * rhs.0
    }
}

impl Mul<Num> for ModInt<Num> {
    type Output = ModInt<Num>;

    fn mul(self, mut rhs: Num) -> ModInt<Num> {
        if rhs >= MOD {
            rhs %= MOD;
        }
        let t = (self.0 * rhs) % MOD;
        ModInt(t)
    }
}

impl MulAssign<Num> for ModInt<Num> {
    fn mul_assign(&mut self, rhs: Num) {
        *self = *self * rhs;
    }
}

impl MulAssign<ModInt<Num>> for ModInt<Num> {
    fn mul_assign(&mut self, rhs: ModInt<Num>) {
        *self = *self * rhs;
    }
}

impl ModInt<Num> {
    pub fn pow(self, e: Num) -> ModInt<Num> {
        let mut result = ModInt(1);
        let mut cur = self;
        let mut e = e;
        while e > 0 {
            if e & 1 == 1 {
                result *= cur;
            }
            e >>= 1;
            cur *= cur;
        }
        result
    }
}


const MOD: usize = 1e9 as usize + 7;

fn main() {
    input! {
        n: usize,
        a: [i64; n]
    }

    let mut acc = vec![0; n + 1];
    for i in 0..n {
        acc[i + 1] += acc[i] + a[i];
    }

    println!("{}", (0..n).map(|x| (acc[n] - 2 * acc[x]).abs()).min().unwrap());
}