Problem:
Score : 300 points

Problem Statement

There are N sightseeing spots on the x-axis, numbered 1, 2, ..., N.
Spot i is at the point with coordinate A_i.
It costs |a - b| yen (the currency of Japan) to travel from a point with coordinate a to another point with coordinate b along the axis.

You planned a trip along the axis.
In this plan, you first depart from the point with coordinate 0, then visit the N spots in the order they are numbered, and finally return to the point with coordinate 0.

However, something came up just before the trip, and you no longer have enough time to visit all the N spots, so you decided to choose some i and cancel the visit to Spot i.
You will visit the remaining spots as planned in the order they are numbered.
You will also depart from and return to the point with coordinate 0 at the beginning and the end, as planned.

For each i = 1, 2, ..., N, find the total cost of travel during the trip when the visit to Spot i is canceled.

Constraints

2 \leq N \leq 10^5

-5000 \leq A_i \leq 5000 (1 \leq i \leq N)

All input values are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N

Output

Print N lines.
In the i-th line, print the total cost of travel during the trip when the visit to Spot i is canceled.

Sample Input 1

3
3 5 -1

Sample Output 1

12
8
10

Spot 1, 2 and 3 are at the points with coordinates 3, 5 and -1, respectively.
For each i, the course of the trip and the total cost of travel when the visit to Spot i is canceled, are as follows:

For i = 1, the course of the trip is 0 \rightarrow 5 \rightarrow -1 \rightarrow 0 and the total cost of travel is 5 + 6 + 1 = 12 yen.

For i = 2, the course of the trip is 0 \rightarrow 3 \rightarrow -1 \rightarrow 0 and the total cost of travel is 3 + 4 + 1 = 8 yen.

For i = 3, the course of the trip is 0 \rightarrow 3 \rightarrow 5 \rightarrow 0 and the total cost of travel is 3 + 2 + 5 = 10 yen.

Sample Input 2

5
1 1 1 2 0

Sample Output 2

4
4
4
2
4

Sample Input 3

6
-679 -2409 -3258 3095 -3291 -4462

Sample Output 3

21630
21630
19932
8924
21630
19288

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

fn main() {
    let n: isize = readln();
    let a: Vec<isize> = readln();
    let mut b: Vec<isize> = Vec::new();
    b.push(0);
    b.extend(a);
    b.push(0);

    let mut init = 0;
    for i in 0..n + 1 {
        init += (b[(i + 1) as usize] - b[i as usize]).abs();
    }

    for i in 1..n + 1 {
        let i = i as isize;
        let mut ans = init;
        {
            let i = i as usize;
            ans -= (b[i] - b[i - 1]).abs();
        }
        {
            let i = i as usize;
            ans -= (b[i + 1] - b[i]).abs();
        }
        {
            let i = i as usize;
            ans += (b[i + 1] - b[i - 1]).abs();
        }
        println!("{}", ans);
    }
}

#[allow(unused_imports)]
use std::cmp::{max, min};
#[allow(unused_imports)]
use std::collections::{HashMap, HashSet, VecDeque};

pub trait FromLn {
    fn fromln(s: &str) -> Self;
}
pub fn readln<T: FromLn>() -> T {
    let mut buf = String::new();
    let _ = ::std::io::stdin().read_line(&mut buf).unwrap();
    T::fromln(buf.trim())
}
pub fn readlns<T: FromLn>(n: usize) -> Vec<T> {
    let mut vs = vec![];
    for _ in 0..n {
        vs.push(readln());
    }
    vs
}
macro_rules! fromln_primitives {
    ($($t:ty),*) => { $(
        impl FromLn for $t {
            fn fromln(s: &str) -> $t {
                s.parse().unwrap()
            }
        }
    )* }
}
fromln_primitives!(
    String,
    bool,
    f32,
    f64,
    isize,
    i8,
    i16,
    i32,
    i64,
    usize,
    u8,
    u16,
    u32,
    u64
);
impl<T> FromLn for Vec<T>
where
    T: FromLn,
{
    fn fromln(s: &str) -> Vec<T> {
        s.split_whitespace().map(T::fromln).collect()
    }
}
impl FromLn for Vec<char> {
    fn fromln(s: &str) -> Vec<char> {
        s.chars().collect()
    }
}
macro_rules! fromln_tuple {
    ($($t:ident),*) => {
        impl<$($t),*> FromLn for ($($t),*) where $($t: FromLn),* {
            fn fromln(s: &str) -> ($($t),*) {
                let mut it = s.split_whitespace();
                let t = ($($t::fromln(it.next().unwrap())),*);
                assert_eq!(it.next(), None);
                t
            }
        }
    }
}
fromln_tuple!(A, B);
fromln_tuple!(A, B, C);
fromln_tuple!(A, B, C, D);
fromln_tuple!(A, B, C, D, E);
fromln_tuple!(A, B, C, D, E, F);
mod comp {
    pub mod math {
        pub mod comb {
            use super::mint::{Mint, MOD};
            pub struct Comb {
                fact: Vec<Mint>,
                factinv: Vec<Mint>,
            }
            impl Comb {}
            #[cfg(test)]
            mod tests {
                use super::*;
                #[test]
                fn test_simple() {
                    let c = Comb::new(100);
                    assert_eq!(Mint::from(336), c.perm(8, 3));
                    assert_eq!(Mint::from(56), c.comb(8, 3));
                    assert_eq!(Mint::from(10), c.multi_comb(3, 3));
                }
                #[test]
                fn test_fact() {
                    let c = Comb::new(100);
                    let p = 8721234;
                    let mut f = Mint::from(1);
                    for i in 1..(p + 1) {
                        f *= i;
                    }
                    assert_eq!(f, c.fact(p));
                }
            }
        }
        pub mod mint {
            use std;
            pub const MOD: u32 = 1000000007;
            #[derive(Debug, Copy, Clone, Eq)]
            pub struct Mint {
                val: u32,
            }
            impl<T: Into<Mint>> std::ops::Add<T> for Mint {
                type Output = Mint;
                fn add(self, other: T) -> Mint {
                    let nval = self.val + other.into().val;
                    Mint {
                        val: if nval >= MOD { nval - MOD } else { nval },
                    }
                }
            }
            impl<T: Into<Mint>> std::ops::Sub<T> for Mint {
                type Output = Mint;
                fn sub(self, other: T) -> Mint {
                    let nval = self.val + MOD - other.into().val;
                    Mint {
                        val: if nval >= MOD { nval - MOD } else { nval },
                    }
                }
            }
            impl<T: Into<Mint>> std::ops::Mul<T> for Mint {
                type Output = Mint;
                fn mul(self, other: T) -> Mint {
                    let nval = self.val as u64 * other.into().val as u64;
                    Mint {
                        val: (nval % (MOD as u64)) as u32,
                    }
                }
            }
            impl<T: Into<Mint>> std::ops::Div<T> for Mint {
                type Output = Mint;
                fn div(self, other: T) -> Mint {
                    self * other.into().inv()
                }
            }
            impl Mint {
                pub fn inv(self) -> Mint {
                    let mut a = self.val as i32;
                    let mut b = MOD as i32;
                    let mut u = 1 as i32;
                    let mut v = 0 as i32;
                    while b != 0 {
                        let t = a / b;
                        a -= t * b;
                        std::mem::swap(&mut a, &mut b);
                        u -= t * v;
                        std::mem::swap(&mut u, &mut v);
                    }
                    Mint {
                        val: if u < 0 { u + MOD as i32 } else { u } as u32,
                    }
                }
            }
            impl PartialEq for Mint {
                fn eq(&self, other: &Mint) -> bool {
                    self.val == other.val
                }
            }
            impl std::fmt::Display for Mint {
                fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
                    self.val.fmt(f)
                }
            }
            macro_rules! impl_signed_mint(( $ ( $ t : ty ) * ) => (
                                      $ (
                                      impl From < $ t > for Mint {
                                      # [ inline ] fn from ( x : $ t ) -> Mint
                                      {
                                      let t = ( x as i64 ) % ( MOD as i64 ) ;
                                      if x >= 0 { Mint { val : t as u32 } }
                                      else {
                                      Mint { val : ( MOD as i64 + t ) as u32 }
                                      } } } ) * ));
            macro_rules! impl_unsigned_mint(( $ ( $ t : ty ) * ) => (
                                        $ (
                                        impl From < $ t > for Mint {
                                        # [ inline ] fn from ( x : $ t ) ->
                                        Mint {
                                        let t = x as u64 % MOD as u64 ; Mint {
                                        val : t as u32 } } } ) * ));
            impl_signed_mint! (i8 i16 i32 i64 isize);
            impl_unsigned_mint! (u8 u16 u32 u64 usize);
            impl<T: Into<Mint>> std::ops::AddAssign<T> for Mint {
                fn add_assign(&mut self, other: T) {
                    *self = *self + other.into();
                }
            }
            impl<T: Into<Mint>> std::ops::SubAssign<T> for Mint {
                fn sub_assign(&mut self, other: T) {
                    *self = *self - other.into();
                }
            }
            impl<T: Into<Mint>> std::ops::MulAssign<T> for Mint {
                fn mul_assign(&mut self, other: T) {
                    *self = *self * other.into();
                }
            }
            impl<T: Into<Mint>> std::ops::DivAssign<T> for Mint {
                fn div_assign(&mut self, other: T) {
                    *self = *self / other.into();
                }
            }
            #[cfg(test)]
            mod tests {
                use super::*;
                #[test]
                fn test_simple() {
                    let a: Mint = Mint::from(3);
                    let b: Mint = Mint::from(1000000000);
                    assert_eq!(Mint::from(3000000000u64 % MOD as u64), a * b);
                }
            }
        }
        pub mod prime {
            #[derive(Copy, Clone, PartialEq, PartialOrd, Ord, Eq, Debug)]
            struct U128 {
                hi: u64,
                lo: u64,
            }
        }
    }
    pub mod data_structure {
        pub mod bit {
            pub struct BIT {
                tree: Vec<i64>,
            }
            pub struct BITRange {
                bit0: BIT,
                bit1: BIT,
            }
            impl BIT {}
            impl BITRange {}
            #[cfg(test)]
            mod tests {
                use super::*;
                #[test]
                fn test_simple() {
                    let mut bit = BIT::new(10);
                    bit.add(2, 1);
                    bit.add(3, 3);
                    bit.add(5, 10);
                    bit.add(0, -4);
                    bit.add(9, -5);
                    assert_eq!(5, bit.get(0, 10));
                    assert_eq!(4, bit.get(2, 4));
                    assert_eq!(1, bit.get(2, 3));
                    assert_eq!(0, bit.get(2, 2));
                    assert_eq!(0, bit.get(2, 0));
                    assert_eq!(-4, bit.get(0, 1));
                    assert_eq!(5, bit.get(5, 10));
                    let mut bit = BITRange::new(10);
                    bit.add(1, 3, 1);
                    bit.add(2, 5, 2);
                    assert_eq!(1, bit.get(1, 2));
                    assert_eq!(4, bit.get(1, 3));
                    assert_eq!(6, bit.get(1, 4));
                    assert_eq!(6, bit.get(0, 4));
                }
            }
        }
        pub mod union_find {
            pub struct UnionFind {
                data: Vec<i32>,
            }
            impl UnionFind {}
            #[cfg(test)]
            mod tests {
                use super::*;
                #[test]
                fn test_simple() {
                    let mut uf = UnionFind::new(3);
                    assert_eq!(1, uf.size(0));
                    assert_eq!(1, uf.size(1));
                    assert_eq!(1, uf.size(2));
                    assert_eq!(0, uf.root(0));
                    assert_eq!(1, uf.root(1));
                    assert_eq!(2, uf.root(2));
                    assert!(!uf.same(1, 2));
                    uf.unite(1, 2);
                    assert_ne!(uf.root(0), uf.root(2));
                    assert_eq!(uf.root(1), uf.root(2));
                    assert_eq!(1, uf.size(0));
                    assert_eq!(2, uf.size(1));
                    assert_eq!(2, uf.size(2));
                    assert!(uf.same(1, 2));
                    uf.unite(0, 1);
                    assert_eq!(uf.root(0), uf.root(2));
                    assert_eq!(uf.root(1), uf.root(2));
                    assert_eq!(3, uf.size(0));
                    assert_eq!(3, uf.size(1));
                    assert_eq!(3, uf.size(2));
                    assert!(uf.same(1, 2));
                    assert!(uf.same(0, 2));
                }
            }
        }
    }
    pub mod util {
        pub mod permutation {
            pub trait Permutation {
                fn next_permutation(&mut self) -> bool;
                fn prev_permutation(&mut self) -> bool;
            }
            impl<T> Permutation for [T]
            where
                T: Ord,
            {
                fn next_permutation(&mut self) -> bool {
                    if self.len() <= 1 {
                        return false;
                    }
                    let mut i = self.len() - 1;
                    while i > 0 && self[i - 1] >= self[i] {
                        i -= 1;
                    }
                    if i == 0 {
                        return false;
                    }
                    let mut j = self.len() - 1;
                    while self[j] <= self[i - 1] {
                        j -= 1;
                    }
                    self.swap(j, i - 1);
                    self[i..].reverse();
                    true
                }
                fn prev_permutation(&mut self) -> bool {
                    if self.len() <= 1 {
                        return false;
                    }
                    let mut i = self.len() - 1;
                    while i > 0 && self[i - 1] <= self[i] {
                        i -= 1;
                    }
                    if i == 0 {
                        return false;
                    }
                    self[i..].reverse();
                    let mut j = self.len() - 1;
                    while self[j - 1] < self[i - 1] {
                        j -= 1;
                    }
                    self.swap(i - 1, j);
                    true
                }
            }
            #[cfg(test)]
            mod tests {
                use super::*;
                #[test]
                fn test_simple() {
                    let mut data = [0, 0, 1, 1, 2];
                    data.next_permutation();
                    assert_eq!(&data, &[0, 0, 1, 2, 1]);
                    data.next_permutation();
                    assert_eq!(&data, &[0, 0, 2, 1, 1]);
                    data.next_permutation();
                    assert_eq!(&data, &[0, 1, 0, 1, 2]);
                    data.next_permutation();
                    assert_eq!(&data, &[0, 1, 0, 2, 1]);
                    data.next_permutation();
                    assert_eq!(&data, &[0, 1, 1, 0, 2]);
                    data.prev_permutation();
                    assert_eq!(&data, &[0, 1, 0, 2, 1]);
                    data.prev_permutation();
                    assert_eq!(&data, &[0, 1, 0, 1, 2]);
                    data.prev_permutation();
                    assert_eq!(&data, &[0, 0, 2, 1, 1]);
                    data.prev_permutation();
                    assert_eq!(&data, &[0, 0, 1, 2, 1]);
                    data.prev_permutation();
                    assert_eq!(&data, &[0, 0, 1, 1, 2]);
                    assert!(!data.prev_permutation());
                }
            }
        }
        pub mod rand {
            use std::{marker, mem};
            use std::io::{self, Read};
            use std::fs::File;
            use std::char;
            #[derive(Debug, Clone, Copy)]
            pub struct Xoroshiro128Rng {
                state: [u64; 2],
            }
            impl Xoroshiro128Rng {}
            impl Rng for Xoroshiro128Rng {
                fn next_u32(&mut self) -> u32 {
                    self.next_u64() as u32
                }
                fn next_u64(&mut self) -> u64 {
                    let s0: u64 = self.state[0];
                    let mut s1: u64 = self.state[1];
                    let result: u64 = s0.wrapping_add(s1);
                    s1 ^= s0;
                    self.state[0] = s0.rotate_left(55) ^ s1 ^ (s1 << 14);
                    self.state[1] = s1.rotate_left(36);
                    result
                }
            }
            pub trait Rand: Sized {
                fn rand<R: Rng>(rng: &mut R) -> Self;
            }
            pub trait Rng {
                fn next_u32(&mut self) -> u32;
                fn next_u64(&mut self) -> u64 {
                    let x = self.next_u32() as u64;
                    let y = self.next_u32() as u64;
                    (y << 32) | x
                }
                fn next_f32(&mut self) -> f32 {
                    const UPPER_MASK: u32 = 1065353216;
                    const LOWER_MASK: u32 = 8388607;
                    let tmp = UPPER_MASK | (self.next_u32() & LOWER_MASK);
                    let result: f32 = unsafe { mem::transmute(tmp) };
                    result - 1.0
                }
                fn next_f64(&mut self) -> f64 {
                    const UPPER_MASK: u64 = 4607182418800017408;
                    const LOWER_MASK: u64 = 4503599627370495;
                    let tmp = UPPER_MASK | (self.next_u64() & LOWER_MASK);
                    let result: f64 = unsafe { mem::transmute(tmp) };
                    result - 1.0
                }
                #[inline(always)]
                fn gen<T: Rand>(&mut self) -> T
                where
                    Self: Sized,
                {
                    Rand::rand(self)
                }
                fn gen_iter<'a, T: Rand>(&'a mut self) -> Generator<'a, T, Self>
                where
                    Self: Sized,
                {
                    Generator {
                        rng: self,
                        _marker: marker::PhantomData,
                    }
                }
                fn shuffle<T>(&mut self, values: &mut [T])
                where
                    Self: Sized,
                {
                    let mut i = values.len();
                    while i >= 2 {
                        i -= 1;
                        values.swap(i, (self.next_u64() as usize) % i);
                    }
                }
            }
            #[derive(Debug)]
            pub struct Generator<'a, T, R: 'a> {
                rng: &'a mut R,
                _marker: marker::PhantomData<fn() -> T>,
            }
            impl<'a, T: Rand, R: Rng> Iterator for Generator<'a, T, R> {
                type Item = T;
                fn next(&mut self) -> Option<T> {
                    Some(self.rng.gen())
                }
            }
            pub struct OsRng {
                reader: File,
            }
            impl OsRng {}
            impl Rng for OsRng {
                fn next_u32(&mut self) -> u32 {
                    let mut dest = [0u8; 4];
                    self.reader.read_exact(&mut dest).unwrap();
                    unsafe { mem::transmute::<[u8; 4], u32>(dest) }
                }
            }
            impl Rand for isize {
                #[inline]
                fn rand<R: Rng>(rng: &mut R) -> isize {
                    if mem::size_of::<isize>() == 4 {
                        rng.gen::<i32>() as isize
                    } else {
                        rng.gen::<i64>() as isize
                    }
                }
            }
            impl Rand for i8 {
                #[inline]
                fn rand<R: Rng>(rng: &mut R) -> i8 {
                    rng.next_u32() as i8
                }
            }
            impl Rand for i16 {
                #[inline]
                fn rand<R: Rng>(rng: &mut R) -> i16 {
                    rng.next_u32() as i16
                }
            }
            impl Rand for i32 {
                #[inline]
                fn rand<R: Rng>(rng: &mut R) -> i32 {
                    rng.next_u32() as i32
                }
            }
            impl Rand for i64 {
                #[inline]
                fn rand<R: Rng>(rng: &mut R) -> i64 {
                    rng.next_u64() as i64
                }
            }
            #[cfg(feature = "i128_support")]
            impl Rand for i128 {
                #[inline]
                fn rand<R: Rng>(rng: &mut R) -> i128 {
                    rng.gen::<u128>() as i128
                }
            }
            impl Rand for usize {
                #[inline]
                fn rand<R: Rng>(rng: &mut R) -> usize {
                    if mem::size_of::<usize>() == 4 {
                        rng.gen::<u32>() as usize
                    } else {
                        rng.gen::<u64>() as usize
                    }
                }
            }
            impl Rand for u8 {
                #[inline]
                fn rand<R: Rng>(rng: &mut R) -> u8 {
                    rng.next_u32() as u8
                }
            }
            impl Rand for u16 {
                #[inline]
                fn rand<R: Rng>(rng: &mut R) -> u16 {
                    rng.next_u32() as u16
                }
            }
            impl Rand for u32 {
                #[inline]
                fn rand<R: Rng>(rng: &mut R) -> u32 {
                    rng.next_u32()
                }
            }
            impl Rand for u64 {
                #[inline]
                fn rand<R: Rng>(rng: &mut R) -> u64 {
                    rng.next_u64()
                }
            }
            #[cfg(feature = "i128_support")]
            impl Rand for u128 {
                #[inline]
                fn rand<R: Rng>(rng: &mut R) -> u128 {
                    ((rng.next_u64() as u128) << 64) | (rng.next_u64() as u128)
                }
            }
            impl Rand for f64 {
                fn rand<R: Rng>(rng: &mut R) -> f64 {
                    rng.next_f64()
                }
            }
            impl Rand for f32 {
                fn rand<R: Rng>(rng: &mut R) -> f32 {
                    rng.next_f32()
                }
            }
            impl Rand for char {
                #[inline]
                fn rand<R: Rng>(rng: &mut R) -> char {
                    const CHAR_MASK: u32 = 2097151;
                    loop {
                        match char::from_u32(rng.next_u32() & CHAR_MASK) {
                            Some(c) => return c,
                            None => {}
                        }
                    }
                }
            }
            impl Rand for bool {
                #[inline]
                fn rand<R: Rng>(rng: &mut R) -> bool {
                    rng.gen::<u8>() & 1 == 1
                }
            }
            macro_rules! tuple_impl(( $ ( $ tyvar : ident ) , * ) => {
                                impl < $ ( $ tyvar : Rand ) , * > Rand for (
                                $ ( $ tyvar ) , * , ) {
                                # [ inline ] fn rand < R : Rng > (
                                _rng : & mut R ) -> ( $ ( $ tyvar ) , * , ) {
                                ( $ ( _rng . gen :: < $ tyvar > (  ) ) , * , )
                                } } });
            impl Rand for () {
                #[inline]
                fn rand<R: Rng>(_: &mut R) -> () {
                    ()
                }
            }
            tuple_impl!(A);
            tuple_impl!(A, B);
            tuple_impl!(A, B, C);
            tuple_impl!(A, B, C, D);
            tuple_impl!(A, B, C, D, E);
            tuple_impl!(A, B, C, D, E, F);
            tuple_impl!(A, B, C, D, E, F, G);
            tuple_impl!(A, B, C, D, E, F, G, H);
            tuple_impl!(A, B, C, D, E, F, G, H, I);
            tuple_impl!(A, B, C, D, E, F, G, H, I, J);
            tuple_impl!(A, B, C, D, E, F, G, H, I, J, K);
            tuple_impl!(A, B, C, D, E, F, G, H, I, J, K, L);
            macro_rules! array_impl({
                                $ n : expr , $ t : ident , $ ( $ ts : ident ,
                                ) * } => {
                                array_impl ! { ( $ n - 1 ) , $ ( $ ts , ) * }
                                impl < T > Rand for [ T ; $ n ] where T : Rand
                                {
                                # [ inline ] fn rand < R : Rng > (
                                _rng : & mut R ) -> [ T ; $ n ] {
                                [
                                _rng . gen :: < $ t > (  ) , $ (
                                _rng . gen :: < $ ts > (  ) ) , * ] } } } ; {
                                $ n : expr , } => {
                                impl < T > Rand for [ T ; $ n ] {
                                fn rand < R : Rng > ( _rng : & mut R ) -> [
                                T ; $ n ] { [  ] } } } ;);
            array_impl!(
                32,
                T,
                T,
                T,
                T,
                T,
                T,
                T,
                T,
                T,
                T,
                T,
                T,
                T,
                T,
                T,
                T,
                T,
                T,
                T,
                T,
                T,
                T,
                T,
                T,
                T,
                T,
                T,
                T,
                T,
                T,
                T,
                T,
            );
            impl<T: Rand> Rand for Option<T> {
                #[inline]
                fn rand<R: Rng>(rng: &mut R) -> Option<T> {
                    if rng.gen() {
                        Some(rng.gen())
                    } else {
                        None
                    }
                }
            }
        }
    }
}