Problem:
Score: 400 points

Problem Statement

To become a millionaire, M-kun has decided to make money by trading in the next N days. Currently, he has 1000 yen and no stocks - only one kind of stock is issued in the country where he lives.

He is famous across the country for his ability to foresee the future. He already knows that the price of one stock in the next N days will be as follows:

A_1 yen on the 1-st day, A_2 yen on the 2-nd day, ..., A_N yen on the N-th day.

In the i-th day, M-kun can make the following trade any number of times (possibly zero), within the amount of money and stocks that he has at the time.

Buy stock: Pay A_i yen and receive one stock.

Sell stock: Sell one stock for A_i yen.

What is the maximum possible amount of money that M-kun can have in the end by trading optimally?

Constraints

2 \leq N \leq 80

100 \leq A_i \leq 200

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 \cdots A_N

Output

Print the maximum possible amount of money that M-kun can have in the end, as an integer.

Sample Input 1

7
100 130 130 130 115 115 150

Sample Output 1

1685

In this sample input, M-kun has seven days of trading. One way to have 1685 yen in the end is as follows:

Initially, he has 1000 yen and no stocks.

Day 1: Buy 10 stocks for 1000 yen. Now he has 0 yen.

Day 2: Sell 7 stocks for 910 yen. Now he has 910 yen.

Day 3: Sell 3 stocks for 390 yen. Now he has 1300 yen.

Day 4: Do nothing.

Day 5: Buy 1 stock for 115 yen. Now he has 1185 yen.

Day 6: Buy 10 stocks for 1150 yen. Now he has 35 yen.

Day 7: Sell 11 stocks for 1650 yen. Now he has 1685 yen.

There is no way to have 1686 yen or more in the end, so the answer is 1685.

Sample Input 2

6
200 180 160 140 120 100

Sample Output 2

1000

In this sample input, it is optimal to do nothing throughout the six days, after which we will have 1000 yen.

Sample Input 3

2
157 193

Sample Output 3

1216

In this sample input, it is optimal to buy 6 stocks in Day 1 and sell them in Day 2, after which we will have 1216 yen.

Solution in Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.io.*;
import java.util.*;

class Main{
    final static long INF = Long.MAX_VALUE / 2;
    final static int MOD = 1_000_000_007;
    final static int SIZE = 1_000_000;
    long[] fac = new long[SIZE];
    long[] inv = new long[SIZE];
    long[] finv = new long[SIZE];
    FastScanner sc = new FastScanner();

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

    void solve(){

        int n = sc.nextInt();
        long[] a = new long[n];
        List<Long> l = new ArrayList<>();

        for(int i = 0; i < n; i++){
            a[i] = sc.nextLong();
        }

        long x = -1;
        long f = 1; // 0:最後に底 1:最後に天井

        for(int i = 0; i < n - 1; i++){
            if(f == 0 && a[i] > x && a[i] > a[i + 1]){
                l.add(a[i]);
                x = a[i];
                f = 1;
            }
            if(f == 1 && a[i] < a[i + 1]){
                l.add(a[i]);
                x = a[i];
                f = 0;
            }
        }

        if(f == 0 && a[n - 1] > x) l.add(a[n - 1]);

        long ans = 1000;

        for(int i = 0; i < l.size() / 2; i++){
            long c = ans / l.get(i * 2);
            ans %= l.get(i * 2);
            ans += c * l.get(i * 2 + 1);
        }

        System.out.println(ans);

    }

    long gcd(long a, long b){ // return aとbの最大公約数
        if(b == 0){
          return a;
        }
        return gcd(b, a % b);
    }

    long lcm(long a, long b){ // return aとbの最小公倍数
        return a * b / gcd(a, b);
    }

    long inv(long a){ // return aの逆元 (mod MOD)
        return pow(a, MOD - 2);
    }

    long pow(long a, long r){ // return a^r (mod MOD)
        long sum = 1;
        while(r > 0){
            if((r & 1) == 1){ // 2進数表記で末尾1の時
                sum *= a;
                sum %= MOD;
            }
            a *= a;
            a %= MOD;
            r >>= 1;
        }
        return sum;
    }

    long modFact(long n){ // retur n! (mod MOD)
        if(n == 0){
            return 1;
        }
        return n * modFact(n - 1) % MOD;
    }

    long fact(long n){ // return n!
        if(n == 0){
            return 1;
        }
        return n * fact(n - 1);
    }

    void initCOMB(){
        fac[0] = fac[1] = 1;
        inv[1] = 1;
        finv[0] = finv[1] = 1;
        for(int i = 2; i < SIZE; i++){
            fac[i] = fac[i - 1] * i % MOD;
            inv[i] = MOD - inv[MOD % i] * (MOD / i) % MOD;
            finv[i] = finv[i - 1] * inv[i] % MOD;
        }
    }

    long modComb(int n, int r){ // return nCr (先にinitCOMB()必要)
        if(n < r || n < 0 || r < 0) return 0;
        return fac[n] * finv[r] % MOD * finv[n - r] % MOD;
    }

    long comb(long n, long r){ // return nCr
        long num = 1;
        for(long i = 1; i <= r; i++){
            num = num * (n - i + 1) / i;
        }
        return num;
    }

    boolean isPrime(long a){ // aの素数判定
        if(a <= 1) return false;
        for(int i = 2; i * i <= a; i++){
            if(a % i == 0) return false;
        }
        return true;
    }

    int lowerBound(long[] a, long v){ // return 配列a内のv以上の要素の内最低の要素のイテレータ
        int r = a.length;
        int l = -1;
        while(r - l > 1){
            int mid = (r + l) / 2;
            if(a[mid] >= v){
                r = mid;
            }else{
                l = mid;
            }
        }
        return r;
    }

    int upperBound(long[] a, long v){ // return 配列a内のvより大きい要素の内最低の要素のイテレータ
        int r = a.length;
        int l = -1;
        while(r - l > 1){
            int mid = (r + l) / 2;
            if(a[mid] > v){
                r = mid;
            }else{
                l = mid;
            }
        }
        return r;
    }

    String nextPermutation(String s){ // return sの次の順列
        ArrayList<Character> list = new ArrayList<>();
        for(int i = 0; i < s.length(); i++) list.add(s.charAt(i));

        int pivotPos = -1;
        char pivot = 0;
        for(int i = list.size() - 2; i >= 0; i--){
            if(list.get(i) < list.get(i+1)){
    			pivotPos = i;
    			pivot = list.get(i);
    			break;
    		}
    	}

        if(pivotPos == -1 && pivot == 0) return null;

        int L = pivotPos + 1;
        int R = list.size() - 1;
    	int minPos = -1;
    	char min = Character.MAX_VALUE;
    	for(int i = R; i >= L; i--){
    		if(pivot < list.get(i)){
    			if(list.get(i) < min){
    				min = list.get(i);
    				minPos = i;
    			}
    		}
    	}

    	Collections.swap(list, pivotPos, minPos);
    	Collections.sort(list.subList(L, R + 1));

    	StringBuilder sb = new StringBuilder();
    	for(int i=0; i<list.size(); i++) sb.append(list.get(i));

    	return sb.toString();
    }

    boolean nextPermutation(long[] a){
        for(int i = a.length - 1; i > 0; i--){
            if(a[i - 1] < a[i]){
                int swapIndex = find(a[i - 1], a, i, a.length - 1);
                long temp = a[swapIndex];
                a[swapIndex] = a[i - 1];
                a[i - 1] = temp;
                Arrays.sort(a, i, a.length);
                return true;
            }
        }
        return false;
    }

    int find(long dest, long[] a, int s, int e){
        if(s == e){
            return s;
        }
        int m = (s + e + 1) / 2;
        return a[m] <= dest ? find(dest, a, s, m - 1) : find(dest, a, m, e);
    }

    void elimination(int[][] a, int[] b) {
        int n = a.length;
        double f;
        for(int k = 0; k < n - 1; k++){
            for(int i = k + 1; i < n; i++){
                f = - a[i][k] / a[k][k];
                for(int j = k + 1; j < n; j++){
                    a[i][j] += f * a[k][j];
                }
                b[i] += f * b[k];
            }
            for(int i = n - 1; i >= 0; i--){
                for(int j = i + 1; j < n; j++){
                    b[i] -= a[i][j] * b[j];
                }
                b[i] = b[i] / a[i][i];
            }
        }
    }



    class SegmentTree{

        //------------------------------------------------------------
        // 2 * n - 1 : 木全体のノード数
        // i + n - 1 : 配列のi番目が対応するノードの番号
        // 2 * i + 1, 2 * i + 2 : i番目のノードの子ノードの番号
        // (i - 1) / 2 : i番目のノードの親ノードの番号
        //
        // int n = sc.nextInt();
        // long[] a = new long[n];
        // for(int i = 0; i < n; i++) a[i] = sc.nextLong();
        // SegmentTree st = new SegmentTree(a);
        // int l = sc.nextInt() - 1;
        // int r = sc.nextInt() - 1;
        // System.out.println(st.query(l, r));
        //------------------------------------------------------------

        final static long INF = Long.MAX_VALUE / 2;

        // long e = INF; // 単位元
        long e = 0;
        long func(long a, long b){ // 処理
            // return Math.min(a, b);
            return a + b;
        }

        int n; // 配列の要素数を超える最小の2のべき乗
        long[] node;

        SegmentTree(long[] a){
            init(a);
        }

        void init(long[] a){ // 配列aで初期化
            n = 1;
            while(n < a.length){
                n *= 2;
            }
            node = new long[2 * n - 1];
            Arrays.fill(node, e);
            for(int i = 0; i < a.length; i++){
                node[i + n - 1] = a[i];
            }
            for(int i = n - 2; i >= 0; i--){
                node[i] = func(node[2 * i + 1], node[2 * i + 2]);
            }
        }

        void update(int p, long v){ // 配列のp番目をvに変更し、木全体を更新
            p = p + n - 1;
            node[p] = v;
            while(p > 0){
                p = (p - 1) / 2;
                node[p] = func(node[2 * p + 1], node[2 * p + 2]);
            }
        }

        long query(int a, int b){ // 区間[a, b)についてクエリを処理
            return query(a, b, 0, 0, n);
        }

        long query(int a, int b, int k, int l, int r){
            if(r <= a || b <= l) return e;
            if(a <= l && r <= b) return node[k];
            return func(query(a, b, 2 * k + 1, l, (l + r) / 2), query(a, b, 2 * k + 2, (l + r) / 2, r));
        }

    }



    class UnionFindTree{

        //------------------------------------------------------------
        // int n = sc.nextInt();
        // int q = sc.nextInt();
        // UnionFindTree uft = new UnionFindTree(n);
        // List<String> ans = new ArrayList<>();
        // for(int i = 0; i < q; i++){
        //     int p = sc.nextInt(); // 0 : union, 1 : same
        //     if(p == 0){
        //         int a = sc.nextInt() - 1;
        //         int b = sc.nextInt() - 1;
        //         uft.union(a, b);
        //     }else if(p == 1){
        //         int a = sc.nextInt() - 1;
        //         int b = sc.nextInt() - 1;
        //         if(uft.same(a, b)) ans.add("Yes");
        //         else ans.add("No");
        //     }
        // }
        // for(String s : ans){
        //     System.out.println(s);
        // }
        //------------------------------------------------------------

        int[] parent; // インデックスにとノードを対応させ、そのルートノードのインデックスを格納
        int[] rank; // parentと同様に、木の高さを格納

        UnionFindTree(int size){
            parent = new int[size];
            rank = new int[size];

            for(int i = 0; i < size; i++){
                makeSet(i);
            }
        }

        void makeSet(int i){
            parent[i] = i;
            rank[i] = 0;
        }

        void union(int x, int y){
            int xRoot = find(x);
            int yRoot = find(y);

            if(rank[xRoot] > rank[yRoot]){ // xが属する木の方が大きい場合
                parent[yRoot] = xRoot;
            }else if(rank[xRoot] < rank[yRoot]){
                parent[xRoot] = yRoot; // yの親をxに更新
            }else{
                parent[yRoot] = xRoot;
                rank[xRoot]++; // 同じ高さの木がルートの子として着くから大きさ++;
            }
        }

        int find(int i){ // iの属するルートを返す
            if(i != parent[i]){
                parent[i] = find(parent[i]);
            }
            return parent[i];
        }

        boolean same(int x, int y){ // xとyが同じ木に属しているかを返す
            return find(x) == find(y);
        }

    }



}



class Pair implements Comparable<Pair>{
    long a, b;
    public Pair(long i, long j){
        a = i;
        b = j;
    }

    @Override
    public int compareTo(Pair p){
        if(this.b < p.b) return -1;
        else if(this.b > p.b) return 1;
        else return 0;
    }

    @Override
    public String toString(){
        return a + " " + b;
    }
}



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());
    }
}