There are n boxes with colored balls on the table. Colors are numbered from 1 to n. i-th box contains ai balls, all of which have color i. You have to write a program that will divide all balls into sets such that:

  * each ball belongs to exactly one of the sets, 
  * there are no empty sets, 
  * there is no set containing two (or more) balls of different colors (each set contains only balls of one color), 
  * there are no two sets such that the difference between their sizes is greater than 1. 



Print the minimum possible number of sets.

Input

The first line contains one integer number n (1 ≤ n ≤ 500).

The second line contains n integer numbers a1, a2, ... , an (1 ≤ ai ≤ 109).

Output

Print one integer number — the minimum possible number of sets.

Examples

Input

3
4 7 8


Output

5


Input

2
2 7


Output

4

Note

In the first example the balls can be divided into sets like that: one set with 4 balls of the first color, two sets with 3 and 4 balls, respectively, of the second color, and two sets with 4 balls of the third color.
import java.awt.*;
import java.io.*;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.util.*;
import java.util.List;

import static java.lang.Math.max;
import static java.lang.Math.min;


public class E implements Runnable{

    // SOLUTION!!!
    // HACK ME PLEASE IF YOU CAN!!!
    // PLEASE!!!
    // PLEASE!!!
    // PLEASE!!!

    private final static Random rnd = new Random();
    private final static String fileName = "";

    final int MAX_A = 1000 * 1000 * 1000;

    private void solve() {
        int n = readInt();
        int[] a = readSortedIntArray(n);

        final int minValue = a[0];

        List<Integer> possibleBlocks = new ArrayList<>();
        for (int block = 1; block <= minValue && block * block <= MAX_A; ++block) {
            possibleBlocks.add(block);
        }
        {
//            long sum = 0;
//            boolean good = true;
//
//            final int nextBlock = (block + 1);
//
//            for (int value : a) {
//                long count = value / nextBlock;
//                if (value % nextBlock != 0) ++count;
//
//                sum += count;
//
//                good &= (count >= (count * nextBlock - value));
//                if (!good) break;
//            }
//
//            if (good) answer = min(answer, sum);
        }

        NavigableMap<Integer, Long> largeBlockTimes = new TreeMap<>();
        NavigableMap<Integer, Integer> largeBlockCounts = new TreeMap<>();

        List<Integer> largeBlocks = new ArrayList<>();
        for (int times = 1; times * times <= minValue; ++times) {
            int block = minValue / times;
            if (block <= MAX_A / block) continue;

            largeBlocks.add(block);
            largeBlocks.add(block - 1);
        }

        Collections.reverse(largeBlocks);
        possibleBlocks.addAll(largeBlocks);
        Collections.reverse(possibleBlocks);

        for (int block : possibleBlocks) {
            long sum = 0;
            boolean good = true;

            final int nextBlock = (block + 1);

            for (int value : a) {
                long count = value / nextBlock;
                if (value % nextBlock != 0) ++count;

                sum += count;

                good &= (count >= (count * nextBlock - value));
                if (!good) break;
            }

            if (good) {
                out.println(sum);
                return;//answer = min(answer, sum);
            }
        }

        out.println(getSum(a));

//        out.println(answer);
    }

    /////////////////////////////////////////////////////////////////////

    private final static boolean FIRST_INPUT_STRING = false;
    private final static boolean MULTIPLE_TESTS = true;
    private final boolean ONLINE_JUDGE = System.getProperty("ONLINE_JUDGE") != null;

    private final static int MAX_STACK_SIZE = 128;

    private final static boolean OPTIMIZE_READ_NUMBERS = false;

    /////////////////////////////////////////////////////////////////////

    public void run(){
        try{
            timeInit();
            Locale.setDefault(Locale.US);

            init();

            if (ONLINE_JUDGE) {
                solve();
            } else {
                do {
                    try {
                        timeInit();
                        solve();
                        time();

                        out.println();
                    } catch (NumberFormatException e) {
                        break;
                    } catch (NullPointerException e) {
                        if (FIRST_INPUT_STRING) break;
                        else throw e;
                    }
                } while (MULTIPLE_TESTS);
            }

            out.close();
            time();
        }catch (Exception e){
            e.printStackTrace(System.err);
            System.exit(-1);
        }
    }

    /////////////////////////////////////////////////////////////////////

    private BufferedReader in;
    private OutputWriter out;
    private StringTokenizer tok = new StringTokenizer("");

    public static void main(String[] args){
        new Thread(null, new E(), "", MAX_STACK_SIZE * (1L << 20)).start();
    }

    /////////////////////////////////////////////////////////////////////

    private void init() throws FileNotFoundException{
        Locale.setDefault(Locale.US);

        if (ONLINE_JUDGE){
            if (fileName.isEmpty()) {
                in = new BufferedReader(new InputStreamReader(System.in));
                out = new OutputWriter(System.out);
            } else {
                in = new BufferedReader(new FileReader(fileName + ".in"));
                out = new OutputWriter(fileName + ".out");
            }
        }else{
            in = new BufferedReader(new FileReader("input.txt"));
            out = new OutputWriter("output.txt");
        }
    }

    ////////////////////////////////////////////////////////////////

    private long timeBegin;

    private void timeInit() {
        this.timeBegin = System.currentTimeMillis();
    }

    private void time(){
        long timeEnd = System.currentTimeMillis();
        System.err.println("Time = " + (timeEnd - timeBegin));
    }

    private void debug(Object... objects){
        if (ONLINE_JUDGE){
            for (Object o: objects){
                System.err.println(o.toString());
            }
        }
    }

    /////////////////////////////////////////////////////////////////////

    private String delim = " ";

    private String readLine() {
        try {
            return in.readLine();
        } catch (IOException e) {
            throw new RuntimeIOException(e);
        }
    }

    private String readString() {
        try {
            while(!tok.hasMoreTokens()){
                tok = new StringTokenizer(readLine());
            }

            return tok.nextToken(delim);
        } catch (NullPointerException e) {
            return null;
        }
    }

    /////////////////////////////////////////////////////////////////

    private final char NOT_A_SYMBOL = '\0';

    private char readChar() {
        try {
            int intValue = in.read();

            if (intValue == -1){
                return NOT_A_SYMBOL;
            }

            return (char) intValue;
        } catch (IOException e) {
            throw new RuntimeIOException(e);
        }
    }

    private char[] readCharArray() {
        return readLine().toCharArray();
    }

    private char[][] readCharField(int rowsCount) {
        char[][] field = new char[rowsCount][];
        for (int row = 0; row < rowsCount; ++row) {
            field[row] = readCharArray();
        }

        return field;
    }

    /////////////////////////////////////////////////////////////////

    private long optimizedReadLong() {
        int sign = 1;
        long result = 0;
        boolean started = false;
        while (true) {
            try {
                int j = in.read();
                if (-1 == j) {
                    if (started) return sign * result;
                    throw new NumberFormatException();
                }

                if (j == '-') {
                    if (started) throw new NumberFormatException();
                    sign = -sign;
                }

                if ('0' <= j && j <= '9') {
                    result = result * 10 + j - '0';
                    started = true;
                } else if (started) {
                    return sign * result;
                }
            } catch (IOException e) {
                throw new RuntimeIOException(e);
            }
        }
    }

    private int readInt() {

        if (!OPTIMIZE_READ_NUMBERS) {
            return Integer.parseInt(readString());
        } else {
            return (int) optimizedReadLong();
        }
    }

    private int[] readIntArray(int size) {
        int[] array = new int[size];

        for (int index = 0; index < size; ++index){
            array[index] = readInt();
        }

        return array;
    }

    private int[] readSortedIntArray(int size) {
        Integer[] array = new Integer[size];

        for (int index = 0; index < size; ++index) {
            array[index] = readInt();
        }
        Arrays.sort(array);

        int[] sortedArray = new int[size];
        for (int index = 0; index < size; ++index) {
            sortedArray[index] = array[index];
        }

        return sortedArray;
    }

    private int[] readIntArrayWithDecrease(int size) {
        int[] array = readIntArray(size);

        for (int i = 0; i < size; ++i) {
            array[i]--;
        }

        return array;
    }

    ///////////////////////////////////////////////////////////////////

    private int[][] readIntMatrix(int rowsCount, int columnsCount) {
        int[][] matrix = new int[rowsCount][];

        for (int rowIndex = 0; rowIndex < rowsCount; ++rowIndex) {
            matrix[rowIndex] = readIntArray(columnsCount);
        }

        return matrix;
    }

    private int[][] readIntMatrixWithDecrease(int rowsCount, int columnsCount) {
        int[][] matrix = new int[rowsCount][];

        for (int rowIndex = 0; rowIndex < rowsCount; ++rowIndex) {
            matrix[rowIndex] = readIntArrayWithDecrease(columnsCount);
        }

        return matrix;
    }

    ///////////////////////////////////////////////////////////////////

    private long readLong() {
        if (!OPTIMIZE_READ_NUMBERS) {
            return Long.parseLong(readString());
        } else {
            return optimizedReadLong();
        }
    }

    private long[] readLongArray(int size) {
        long[] array = new long[size];

        for (int index = 0; index < size; ++index){
            array[index] = readLong();
        }

        return array;
    }

    ////////////////////////////////////////////////////////////////////

    private double readDouble() {
        return Double.parseDouble(readString());
    }

    private double[] readDoubleArray(int size) {
        double[] array = new double[size];

        for (int index = 0; index < size; ++index){
            array[index] = readDouble();
        }

        return array;
    }

    ////////////////////////////////////////////////////////////////////

    private BigInteger readBigInteger() {
        return new BigInteger(readString());
    }

    private BigDecimal readBigDecimal() {
        return new BigDecimal(readString());
    }

    /////////////////////////////////////////////////////////////////////

    private Point readPoint() {
        int x = readInt();
        int y = readInt();
        return new Point(x, y);
    }

    private Point[] readPointArray(int size) {
        Point[] array = new Point[size];

        for (int index = 0; index < size; ++index){
            array[index] = readPoint();
        }

        return array;
    }

    /////////////////////////////////////////////////////////////////////

    @Deprecated
    private List<Integer>[] readGraph(int vertexNumber, int edgeNumber) {
        @SuppressWarnings("unchecked")
        List<Integer>[] graph = new List[vertexNumber];

        for (int index = 0; index < vertexNumber; ++index){
            graph[index] = new ArrayList<>();
        }

        while (edgeNumber-- > 0){
            int from = readInt() - 1;
            int to = readInt() - 1;

            graph[from].add(to);
            graph[to].add(from);
        }

        return graph;
    }

    private static class GraphBuilder {

        final int size;
        final List<Integer>[] edges;

        static GraphBuilder createInstance(int size) {
            List<Integer>[] edges = new List[size];
            for (int v = 0; v < size; ++v) {
                edges[v] = new ArrayList<>();
            }

            return new GraphBuilder(edges);
        }

        private GraphBuilder(List<Integer>[] edges) {
            this.size = edges.length;
            this.edges = edges;
        }

        public void addEdge(int from, int to) {
            addDirectedEdge(from, to);
            addDirectedEdge(to, from);
        }

        public void addDirectedEdge(int from, int to) {
            edges[from].add(to);
        }

        public int[][] build() {
            int[][] graph = new int[size][];
            for (int v = 0; v < size; ++v) {
                List<Integer> vEdges = edges[v];
                graph[v] = castInt(vEdges);
            }

            return graph;
        }
    }

    /////////////////////////////////////////////////////////////////////

    private static class IntIndexPair {

        static Comparator<IntIndexPair> increaseComparator = new Comparator<E.IntIndexPair>() {

            @Override
            public int compare(E.IntIndexPair indexPair1, E.IntIndexPair indexPair2) {
                int value1 = indexPair1.value;
                int value2 = indexPair2.value;

                if (value1 != value2) return value1 - value2;

                int index1 = indexPair1.index;
                int index2 = indexPair2.index;

                return index1 - index2;
            }
        };

        static Comparator<IntIndexPair> decreaseComparator = new Comparator<E.IntIndexPair>() {

            @Override
            public int compare(E.IntIndexPair indexPair1, E.IntIndexPair indexPair2) {
                int value1 = indexPair1.value;
                int value2 = indexPair2.value;

                if (value1 != value2) return -(value1 - value2);

                int index1 = indexPair1.index;
                int index2 = indexPair2.index;

                return index1 - index2;
            }
        };

        static IntIndexPair[] from(int[] array) {
            IntIndexPair[] iip = new IntIndexPair[array.length];
            for (int i = 0; i < array.length; ++i) {
                iip[i] = new IntIndexPair(array[i], i);
            }

            return iip;
        }

        int value, index;

        IntIndexPair(int value, int index) {
            super();
            this.value = value;
            this.index = index;
        }

        int getRealIndex() {
            return index + 1;
        }
    }

    private IntIndexPair[] readIntIndexArray(int size) {
        IntIndexPair[] array = new IntIndexPair[size];

        for (int index = 0; index < size; ++index) {
            array[index] = new IntIndexPair(readInt(), index);
        }

        return array;
    }

    /////////////////////////////////////////////////////////////////////

    private static class OutputWriter extends PrintWriter {

        final int DEFAULT_PRECISION = 12;

        private int precision;
        private String format, formatWithSpace;

        {
            precision = DEFAULT_PRECISION;

            format = createFormat(precision);
            formatWithSpace = format + " ";
        }

        OutputWriter(OutputStream out) {
            super(out);
        }

        OutputWriter(String fileName) throws FileNotFoundException {
            super(fileName);
        }

        int getPrecision() {
            return precision;
        }

        void setPrecision(int precision) {
            precision = max(0, precision);
            this.precision = precision;

            format = createFormat(precision);
            formatWithSpace = format + " ";
        }

        String createFormat(int precision){
            return "%." + precision + "f";
        }

        @Override
        public void print(double d){
            printf(format, d);
        }

        void printWithSpace(double d){
            printf(formatWithSpace, d);
        }

        void printAll(double...d){
            for (int i = 0; i < d.length - 1; ++i){
                printWithSpace(d[i]);
            }

            print(d[d.length - 1]);
        }

        @Override
        public void println(double d){
            printlnAll(d);
        }

        void printlnAll(double... d){
            printAll(d);
            println();
        }
    }

    /////////////////////////////////////////////////////////////////////

    private static class RuntimeIOException extends RuntimeException {

        /**
         *
         */
        private static final long serialVersionUID = -6463830523020118289L;

        RuntimeIOException(Throwable cause) {
            super(cause);
        }
    }

    /////////////////////////////////////////////////////////////////////
    //////////////// Some useful constants and functions ////////////////
    /////////////////////////////////////////////////////////////////////

    private static final int[][] steps = {{-1, 0}, {1, 0}, {0, -1}, {0, 1}};
    private static final int[][] steps8 = {
            {-1, 0}, {1, 0}, {0, -1}, {0, 1},
            {-1, -1}, {1, 1}, {1, -1}, {-1, 1}
    };

    private static boolean checkCell(int row, int rowsCount, int column, int columnsCount) {
        return checkIndex(row, rowsCount) && checkIndex(column, columnsCount);
    }

    private static boolean checkIndex(int index, int lim){
        return (0 <= index && index < lim);
    }

    /////////////////////////////////////////////////////////////////////

    private static boolean checkBit(int mask, int bit){
        return (mask & (1 << bit)) != 0;
    }
    private static boolean checkBit(long mask, int bit){
        return (mask & (1L << bit)) != 0;
    }

    /////////////////////////////////////////////////////////////////////

    private static long getSum(int[] array) {
        long sum = 0;
        for (int value: array) {
            sum += value;
        }

        return sum;
    }

    private static Point getMinMax(int[] array) {
        int min = array[0];
        int max = array[0];

        for (int index = 0, size = array.length; index < size; ++index, ++index) {
            int value = array[index];

            if (index == size - 1) {
                min = min(min, value);
                max = max(max, value);
            } else {
                int otherValue = array[index + 1];

                if (value <= otherValue) {
                    min = min(min, value);
                    max = max(max, otherValue);
                } else {
                    min = min(min, otherValue);
                    max = max(max, value);
                }
            }
        }

        return new Point(min, max);
    }

    /////////////////////////////////////////////////////////////////////

    private static int[] getPrimes(int n) {
        boolean[] used = new boolean[n];
        used[0] = used[1] = true;

        int size = 0;
        for (int i = 2; i < n; ++i) {
            if (!used[i]) {
                ++size;
                for (int j = 2 * i; j < n; j += i) {
                    used[j] = true;
                }
            }
        }

        int[] primes = new int[size];
        for (int i = 0, cur = 0; i < n; ++i) {
            if (!used[i]) {
                primes[cur++] = i;
            }
        }

        return primes;
    }

    /////////////////////////////////////////////////////////////////////

    private static long lcm(long a, long b) {
        return a / gcd(a, b) * b;
    }

    private static long gcd(long a, long b) {
        return (a == 0 ? b : gcd(b % a, a));
    }

    /////////////////////////////////////////////////////////////////////

    private static class MultiSet<ValueType> {

        public static <ValueType> MultiSet<ValueType> createMultiSet() {
            Map<ValueType, Integer> multiset = new HashMap<>();
            return new MultiSet<>(multiset);
        }

        private final Map<ValueType, Integer> multiset;
        private int size;

        public MultiSet(Map<ValueType, Integer> multiset) {
            this.multiset = multiset;
            this.size = 0;
        }

        public int size() {
            return size;
        }

        public void inc(ValueType value) {
            int count = get(value);
            multiset.put(value, count + 1);

            ++size;
        }

        public void dec(ValueType value) {
            int count = get(value);
            if (count == 0) return;

            if (count == 1) multiset.remove(value);
            else multiset.put(value, count - 1);

            --size;
        }

        public int get(ValueType value) {
            Integer count = multiset.get(value);
            return (count == null ? 0 : count);
        }
    }

    /////////////////////////////////////////////////////////////////////

    private static class IdMap<KeyType> extends HashMap<KeyType, Integer> {

        /**
         *
         */
        private static final long serialVersionUID = -3793737771950984481L;

        public IdMap() {
            super();
        }

        int getId(KeyType key) {
            Integer id = super.get(key);
            if (id == null) {
                super.put(key, id = size());
            }

            return id;
        }
    }

    /////////////////////////////////////////////////////////////////////

    private static int[] castInt(List<Integer> list) {
        int[] array = new int[list.size()];
        for (int i = 0; i < array.length; ++i) {
            array[i] = list.get(i);
        }

        return array;
    }

    private static long[] castLong(List<Long> list) {
        long[] array = new long[list.size()];
        for (int i = 0; i < array.length; ++i) {
            array[i] = list.get(i);
        }

        return array;
    }

    /////////////////////////////////////////////////////////////////////

    /**
     * Generates list with values 0..<n
     * @param n - exclusive limit of sequence
     */
    private static List<Integer> order(int n) {
        List<Integer> sequence = new ArrayList<>();
        for (int i = 0; i < n; ++i) {
            sequence.add(i);
        }

        return sequence;
    }
}

