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 Go (1.6) (judge verdict: Runtime Error)

package main

import (
	"bufio"
	"fmt"
	"os"
	"strconv"
)

func main() {
	sc := bufio.NewScanner(os.Stdin)
	sc.Split(bufio.ScanWords)

	nItems := scanInt(sc)

	ns := make([]int64, nItems)
	for i := 0; i < len(ns); i++ {
		ns[i] = int64(scanInt(sc))
	}

	m := ns[0]
	for i := 1; i < len(ns); i++ {
		m = lcm(m, ns[i])
	}
	m -= 1

	f := int64(0)
	for _, n := range ns {
		if n-1 != m%n {
			panic("diff")
		}
		f += m % n
	}

	fmt.Println(f)
}

func scanInt(sc *bufio.Scanner) int {
	sc.Scan()
	v, _ := strconv.Atoi(sc.Text())
	return v
}

func lcm(a, b int64) int64 {
	if a > b {
		b, a = a, b
	}
	return a * (b / gcd(a, b))
}

func gcd(a, b int64) int64 {
	if a > b {
		b, a = a, b
	}

	for b%a != 0 {
		b, a = a, b%a
	}
	return a
}