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 PHP7 (7.0.15) (judge verdict: Runtime Error)

<?php
$n = trim(fgets(STDIN));
$a = explode(' ', trim(fgets(STDIN)));
for ($i = 0; $i < $n; $i++) {
    $a[$i] = (int)$a[$i];
}

$lcm = 1;
for ($i = 0; $i < $n; $i++) {
    $lcm = lcm($lcm, $a[$i]);
}

$ans = 0;
for ($i = 0; $i < $n; $i++) {
    $ans += ($lcm - 1) % $a[$i];
}

echo $ans . PHP_EOL;

function gcd($m, $n){
    if($n > $m) list($m, $n) = array($n, $m);

    while($n !== 0){
        $tmp_n = $n;
        $n = $m % $n;
        $m = $tmp_n;
    }
    return $m;
}

function lcm($m, $n){
    return $m * $n / gcd($m, $n);
}