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 Kotlin (1.3.71) (judge verdict: Wrong Answer)

fun main() {
    nextInt()
    val n = nextLongList()
    var m = n.first()
    (1..n.lastIndex).forEach {
        val v = n[it]
        if (m % v == 0L) return@forEach
        m *= v / gcd(m, v)
    }
    m -= 1
    println(n.map {
        m.rem(it)
    }.sum())
}

// # Utils
// ## Input
fun next() = readLine()!!
fun nextInt() = next().toInt()
fun nextLong() = next().toLong()
fun nextDouble() = next().toDouble()
fun nextList() = next().split(" ")
fun nextIntList() = next().split(" ").map(String::toInt)
fun nextLongList() = next().split(" ").map(String::toLong)
fun nextDoubleList() = next().split(" ").map(String::toDouble)

// ## Array
inline fun <reified T> sizedArray(size: Int, default: T) = Array(size) { default }
inline fun <reified T> sized2DArray(row: Int, column: Int, default: T) = Array(row) { Array(column) { default } }

// ## mod^-1
//    [NOTE] CANNOT use this for 0, mod, 2mod, 3mod ...(return wrong value)
fun modinv(num: Long, mod: Long): Long {
    var a = num
    var b = mod
    var u = 1L
    var v = 0L
    while (b > 0) {
        val t = a.div(b)
        a -= t * b
        a = b.also { b = a } // swap a and b
        u -= t * v
        u = v.also { v = u } // swap u and v
    }
    u %= mod
    if (u < 0) u += mod
    return u
}

fun gcd(x: Int, y: Int): Int {
    fun innerGcd(x: Int, y: Int): Int {
        return if (x % y == 0) y else innerGcd(y, x % y)
    }
    return if (x >= y) innerGcd(x, y) else innerGcd(y, x)
}

fun gcd(x: Long, y: Long): Long {
    fun innerGcd(x: Long, y: Long): Long {
        return if (x % y == 0L) y else innerGcd(y, x % y)
    }
    return if (x >= y) innerGcd(x, y) else innerGcd(y, x)
}

// classes
class UnionFindTree(val size: Int) {
    private val r = sizedArray(size, -1)
    fun root(x: Int): Int {
        if (r[x] < 0) return x
        return root(r[x])
    }

    fun unite(x: Int, y: Int) {
        var rx = root(x)
        var ry = root(y)
        if (rx == ry) return
        if (r[rx] > r[ry]) {
            rx = ry.also { ry = rx }
        }
        r[rx] += r[ry]
        r[ry] = rx
    }

    fun size(x: Int) = -r[root(x)]

    override fun toString(): String {
        return r.joinToString(separator = ", ")
    }
}