Problem:
Score : 300 points

Problem Statement

You are given N positive integers a_1, a_2, ..., a_N.

For a non-negative integer m, let f(m) = (m\ mod\ a_1) + (m\ mod\ a_2) + ... + (m\ mod\ a_N).

Here, X\ mod\ Y denotes the remainder of the division of X by Y.

Find the maximum value of f.

Constraints

All values in input are integers.

2 \leq N \leq 3000

2 \leq a_i \leq 10^5

Input

Input is given from Standard Input in the following format:

N
a_1 a_2 ... a_N

Output

Print the maximum value of f.

Sample Input 1

3
3 4 6

Sample Output 1

10

f(11) = (11\ mod\ 3) + (11\ mod\ 4) + (11\ mod\ 6) = 10 is the maximum value of f.

Sample Input 2

5
7 46 11 20 11

Sample Output 2

90

Sample Input 3

7
994 518 941 851 647 2 581

Sample Output 3

4527

Solution in Rust (1.15.1) (judge verdict: Wrong Answer)

#![allow(unused)]

use std::{cell, cmp, collections, convert, fmt, io, iter, ops, str};

use cell::{Cell, RefCell};
use cmp::Ordering::{Equal, Greater, Less};
use collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, LinkedList, VecDeque};
use io::{Read, Write};

#[cfg(feature = "debug")]
macro_rules! debug {
    ($($args: tt)*) => { eprint!($($args)*) };
}

#[cfg(feature = "debug")]
macro_rules! debugln {
    ($($args: tt)*) => { eprintln!($($args)*) };
}

#[cfg(not(feature = "debug"))]
macro_rules! debug {
    ($($args:tt)*) => {};
}

#[cfg(not(feature = "debug"))]
macro_rules! debugln {
    ($($args:tt)*) => {};
}

macro_rules! vmax {
    ($x: expr, $y: expr) => { cmp::max($x, $y) };
    ($x: expr, $($args: expr),*) => { cmp::max($x, vmax!($($args),*)) };
}

macro_rules! vmin {
    ($x: expr, $y: expr) => { cmp::min($x, $y) };
    ($x: expr, $($args: expr),*) => { cmp::min($x, vmin!($($args),*)) };
}

fn main() {
    let _ = parse_line::<usize>();
    let ary = parse_vec::<u64>();

    let f = |m: u64| -> u64 { ary.iter().map(|a| m % a).sum::<u64>() };

    let lcm = ary.iter().skip(1).fold(ary[0], |acc, &x| lcm(acc, x));

    println!("{}", f(lcm - 1));
}

fn gcd(a: u64, b: u64) -> u64 {
    if a < b {
        gcd(b, a)
    } else if b == 0 {
        a
    } else {
        gcd(b, a % b)
    }
}

fn lcm(a: u64, b: u64) -> u64 {
    a / gcd(a, b) * b
}

#[cfg(test)]
mod tests {
    use super::*;

    #[test]
    fn test() {
        //
    }
}

fn read_line() -> String {
    let mut buf = String::new();
    io::stdin().read_line(&mut buf).unwrap();
    buf.trim().to_owned()
}

fn read_word() -> String {
    const CAPACITY: usize = 16;

    let mut stdin = io::stdin();
    let mut byte: [u8; 1] = [0];

    loop {
        let mut buf = Vec::with_capacity(CAPACITY);

        loop {
            let res = stdin.read(&mut byte);

            if res.unwrap_or(0) == 0 || byte[0] <= b' ' {
                break;
            } else {
                buf.push(byte[0]);
            }
        }

        if !buf.is_empty() {
            return String::from_utf8(buf).unwrap();
        }
    }
}

fn parse_line<T: str::FromStr>() -> T {
    read_line().parse().ok().unwrap()
}

fn parse_word<T: str::FromStr>() -> T {
    read_word().parse().ok().unwrap()
}

fn parse_vec<T: str::FromStr>() -> Vec<T> {
    read_line()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}

fn flush() {
    io::stdout().flush();
}

fn next_prime(x: i32) -> i32 {
    for i in (x + 1).. {
        if is_prime(i) {
            return i;
        }
    }

    panic!("attempt to add with overflow");
}

fn is_prime(x: i32) -> bool {
    let ceil = f64::from(x).sqrt().ceil() as i32;
    x == 2 || (2..(ceil + 1)).all(|i| x % i != 0)
}

fn bit_high(bits: u64, pos: u64) -> bool {
    bits & (1 << pos) != 0
}