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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.net.ConnectException;
import java.rmi.dgc.Lease;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Deque;
import java.util.HashMap;
import java.util.HashSet;
import java.util.List;
import java.util.Map;
import java.util.NoSuchElementException;
import java.util.Objects;
import java.util.Set;
import java.util.Stack;
import java.util.TreeMap;
import java.util.TreeSet;

import static java.util.Comparator.*;

public class Main {
	public static void main(String[] args) {
		Main main = new Main();
		main.solve();
		main.out.close();
	}

	// ======================================================================
//	final int MOD = (int)(1e9) + 7;
	// 素因数分解した結果の、素数と指数の組み合わせをセットするマップ
	Map<Integer, Integer> wk, map = new HashMap<>();
	Sieve sieve = new Sieve(1000000);	// １０の６乗まで処理する
	public void solve() {
		int N = ni();
		int[] A = ni(N);
		int cnt;
		for (int i = 0; i < N; i++) {
			wk = sieve.factor(A[i]);
			for(int key : wk.keySet()) {
				cnt = wk.get(key);
				// 指数はその素数の中の最大値を残す　→　最小公倍数の計算で使う
				map.merge(key, cnt, (v1, v2) -> { return Math.max(v1, v2); });
			}
		}
		// 最小公倍数の計算
		long lcm = 1;
		for(int key : map.keySet()) {
			cnt = map.get(key);
			for (int i = 0; i < cnt; i++) {
//				lcm = (lcm * key) % MOD;
				lcm = (lcm * key);
			}
		}
		lcm--;
		long ans = 0;
		for (int i = 0; i < N; i++) {
			ans += lcm % A[i];
		}
		out.println(ans);
	}
	//-----------------------------------
	// 多くの数を素因数分解する場合に使うクラス
	//-----------------------------------
	class Sieve {
		int n;
		int[] f;					// エラトステネスの篩(ふるい）の変形（割った素数を保存する）
		List<Integer> primes = new ArrayList<>();					// 素数の配列
		
		// 初期化　n 以下の数を素数判定する　→　これを作るのは１回だけ
		public Sieve(int n) {
			this.n = n;
			f = new int[n+10];
			for (int i = 0; i < f.length; i++) {
				f[i] = i;					// 初期値として全て素数とする
			}
			f[0] = f[1] = -1;						// ０，１は素数でない
			for(int i = 2; i*i <= n; i++) {
				if(f[i] != i)		continue;			// 素数でない
				primes.add(i);					// 素数を保存
				for (int j = i*i; j <= n; j += i) {
					if(f[j] == j)		f[j] = i;		// 割った素数を保存（最初に割った素数）
				}
			}
		}
		// 素数判定
		boolean isPrime(int x) {
			return f[x] == x;
		}
		// 素因数分解　引数  12 --> 2 * 2 * 3　３つ素数がセットされたリストを返す
		List<Integer> factorList(int arg) {
			int x = arg;
			List<Integer> ans = new ArrayList<>();
			while(x != 1) {
				ans.add(f[x]);
				if(f[x] == 0) {
					out.println("zero devide  x = " + x + "  arg = " + arg);
					x = 1;
				} else {
					x /= f[x];
				}
			}
			return ans;
		}
		// 素因数分解　引数　12 --> 2 * 2 * 3  Map で　(2, 2) (3, 1) を返す
		Map<Integer, Integer> factor(int x) {
			Map<Integer, Integer> ans = new HashMap<>();
			List<Integer> flist = factorList(x);
			if(flist.size() == 0)	return ans;
			for(int p : flist) {
				ans.merge(p, 1, Integer::sum);
			}
			return ans;
		}
	}
		
	// ------------------------------------------
	// ライブラリ
	// ------------------------------------------
	// Print
	private PrintWriter out = new PrintWriter(System.out);

	// Scanner
	private FastScanner scan = new FastScanner();

	int ni() {
		return scan.nextInt();
	}

	int[] ni(int n) {
		int[] a = new int[n];
		for (int i = 0; i < n; i++) {
			a[i] = ni();
		}
		return a;
	}

	int[][] ni(int y, int x) {
		int[][] a = new int[y][x];
		for (int i = 0; i < y; i++) {
			for (int j = 0; j < x; j++) {
				a[i][j] = ni();
			}
		}
		return a;
	}

	long nl() {
		return scan.nextLong();
	}

	long[] nl(int n) {
		long[] a = new long[n];
		for (int i = 0; i < n; i++) {
			a[i] = nl();
		}
		return a;
	}

	long[][] nl(int y, int x) {
		long[][] a = new long[y][x];
		for (int i = 0; i < y; i++) {
			for (int j = 0; j < x; j++) {
				a[i][j] = nl();
			}
		}
		return a;
	}

	String ns() {
		return scan.next();
	}

	String[] ns(int n) {
		String[] a = new String[n];
		for (int i = 0; i < n; i++) {
			a[i] = ns();
		}
		return a;
	}

	String[][] ns(int y, int x) {
		String[][] a = new String[y][x];
		for (int i = 0; i < y; i++) {
			for (int j = 0; j < x; j++) {
				a[i][j] = ns();
			}
		}
		return a;
	}
}

class FastScanner {
	private final InputStream in = System.in;
	private final byte[] buffer = new byte[1024];
	private int ptr = 0;
	private int buflen = 0;

	private boolean hasNextByte() {
		if (ptr < buflen) {
			return true;
		} else {
			ptr = 0;
			try {
				buflen = in.read(buffer);
			} catch (IOException e) {
				e.printStackTrace();
			}
			if (buflen <= 0) {
				return false;
			}
		}
		return true;
	}

	private int readByte() {
		if (hasNextByte())
			return buffer[ptr++];
		else
			return -1;
	}

	private static boolean isPrintableChar(int c) {
		return 33 <= c && c <= 126;
	}

	public boolean hasNext() {
		while (hasNextByte() && !isPrintableChar(buffer[ptr]))
			ptr++;
		return hasNextByte();
	}

	public String next() {
		if (!hasNext())
			throw new NoSuchElementException();
		StringBuilder sb = new StringBuilder();
		int b = readByte();
		while (isPrintableChar(b)) {
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}

	public long nextLong() {
		if (!hasNext())
			throw new NoSuchElementException();
		long n = 0;
		boolean minus = false;
		int b = readByte();
		if (b == '-') {
			minus = true;
			b = readByte();
		}
		if (b < '0' || '9' < b) {
			throw new NumberFormatException();
		}
		while (true) {
			if ('0' <= b && b <= '9') {
				n *= 10;
				n += b - '0';
			} else if (b == -1 || !isPrintableChar(b)) {
				return minus ? -n : n;
			} else {
				throw new NumberFormatException();
			}
			b = readByte();
		}
	}

	public int nextInt() {
		long nl = nextLong();
		if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE)
			throw new NumberFormatException();
		return (int) nl;
	}

	public double nextDouble() {
		return Double.parseDouble(next());
	}
}