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 1.8.0) (judge verdict: Wrong Answer)

import java.io.*;import java.util.*;import java.math.*;
public class Main
{
	static long mod=1000000007l;
    static int max=Integer.MAX_VALUE,min=Integer.MIN_VALUE;
    static long maxl=Long.MAX_VALUE,minl=Long.MIN_VALUE;
    static BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
    static StringTokenizer st;
    static StringBuilder sb;
    
    
    static public void main(String[] args)throws Exception
    {	
    	st=new StringTokenizer(br.readLine());
    	int n=i();
    	int ar[]=ari(n);
    	LinkedList<Integer> al=new LinkedList<>();
    	for(int x:ar)
    	{
    		if(al.size()>0&&al.getLast()==x) {}
    		else al.add(x);
    	}
    	int a[]=new int[al.size()];
    	int i=-1;
    	if(al.size()==1)
    	{
    		pl(1000);
    		System.exit(0);
    	}
    	for(int e:al)a[++i]=e;
    		int m=1000;
    		n=a.length;
    		int c=0;
    		int t=0;
    		int val=1000;
    		//pl(al);
    		for(int x=0;x<n;x++)
    		{
    			if(c==0)
    			{
	    			if(x==0)
	    			{
	    				if(a[x+1]>=a[x])
	    				{t=a[x];
	    					c=1;
	    				}
	    			}
	    			else if(x!=n-1)
	    			{
	    				if(a[x+1]>=a[x]&&a[x-1]>=a[x])
	    					{
	    					t=a[x];
	    					c=1;
	    					}
	    			}
	    			//c=1;
    			}
    			else
    			{
	    			if(x==n-1)
	    			{
	    				if(a[x-1]<=a[x])
	    				{
	    					int s=val/t;
	    					val=val%t;
	    					//pl(val);
	    					val+=(a[x]*s);
	    					//pl(s+"    "+val+" "+a[x]);
	    					c=0;
	    				}
	    			}
	    			else
	    			{
	    				if(a[x+1]<=a[x]&&a[x-1]<=a[x])
	    				{
	    					int s=val/t;
	    					val=val%t;
	    					val+=a[x]*s;
	    					c=0;
	    				}
	    			}
	    			//c=0;
	    			//pl(val+" "+t);
    			}
    		}
    		pl(val);
    	
    }
    
    static boolean f(int a,int b,int c,int k)
    {
    	
    	if(b>a&&c>b)return true;
    	if(k==0)return false;
    	return f(a*2,b,c,k-1)||f(a,b*2,c,k-1)||
    			f(a,b,c*2,k-1);
    }
    
    static void s(int a){sb.append(a);}
    static void s(String a){sb.append(a);}
    static void s(double a){sb.append(a);}
    static void s(char a){sb.append(a);}
    static void s(long a){sb.append(a);}
    static int max(int a,int b){return a>b?a:b;}
    static int min(int a,int b){return a<b?a:b;}
    static int abs(int a){return Math.abs(a);}
    static long max(long a,long b){return a>b?a:b;}
    static long min(long a,long b){return a<b?a:b;}
    static long abs(long a){return Math.abs(a);}
    static int sq(int a){return (int)Math.sqrt(a);}
    static long sq(long a){return (long)Math.sqrt(a);}
    static int gcd(int a,int b){return b==0?a:gcd(b,a%b);}
//    static void g(int i)
//    {
//    	for(int e:ar[i])
//    	{
//    		if(e==i)continue;
//    		al[i].add(e);
//    		g(e);
//    	}
//    }
    static boolean pa(String s,int i,int j)
    {
    	while(i<j)if(s.charAt(i++)!=s.charAt(j--))return false;
    	return true;
    }
    static int ncr(int n,int c,long m)
    {
        long a=1l;
        for(int x=n-c+1;x<=n;x++)a=((a*x)%m);
        long b=1l;
        for(int x=2;x<=c;x++)b=((b*x)%m);
        return (int)((a*(div((int)b,m-2,m)%m))%m);
    }
    static boolean[] sieve(int n)
    {
        boolean bo[]=new boolean[n+1];
        bo[0]=true;bo[1]=true;
        for(int x=4;x<=n;x+=2)bo[x]=true;
        for(int x=3;x*x<=n;x+=2)if(!bo[x])for(int y=x*x;y<=n;y+=x)bo[y]=true;
        return bo;
    }
    static int[] fac(int n)
    {
        int bo[]=new int[n+1];
        for(int x=1;x<=n;x++)for(int y=x;y<=n;y+=x)bo[y]++;
        return bo;
    }
    static long div(long a,long b,long m) 
    {
        long r=1l;
        a%=m;  
        while(b>0)
        {
            if((b&1)==1)r=(r*a)%m; 
            b>>=1;
            a=(a*a)%m;  
        } 
        return r; 
    }
    static int i()throws IOException
    {
        if(!st.hasMoreTokens()) st=new StringTokenizer(br.readLine());
        return Integer.parseInt(st.nextToken());
    }
    static long l()throws IOException
    {
        if(!st.hasMoreTokens())st=new StringTokenizer(br.readLine());
        return Long.parseLong(st.nextToken());
    }
    static String s()throws IOException
    {
        if(!st.hasMoreTokens())st=new StringTokenizer(br.readLine());
        return st.nextToken();
    }
    static double d()throws IOException
    {
        if(!st.hasMoreTokens())st=new StringTokenizer(br.readLine());
        return Double.parseDouble(st.nextToken());
    }
    static void p(Object p){System.out.print(p);}
    static void p(String p){System.out.print(p);}
    static void p(int p){System.out.print(p);}
    static void p(double p){System.out.print(p);}
    static void p(long p){System.out.print(p);}
    static void p(char p){System.out.print(p);}
    static void p(boolean p){System.out.print(p);}
    static void pl(Object p){System.out.println(p);}
    static void pl(String p){System.out.println(p);}
    static void pl(int p){System.out.println(p);}
    static void pl(char p){System.out.println(p);}
    static void pl(double p){System.out.println(p);}
    static void pl(long p){System.out.println(p);}
    static void pl(boolean p){System.out.println(p);}
    static void pl(){System.out.println();}
    static int[] ari(int n)throws IOException
    {
        int ar[]=new int[n];
        if(!st.hasMoreTokens())st=new StringTokenizer(br.readLine());
        for(int x=0;x<n;x++)ar[x]=Integer.parseInt(st.nextToken());
        return ar;
    }
    static int[][] ari(int n,int m)throws IOException
    {
        int ar[][]=new int[n][m];
        for(int x=0;x<n;x++)
        {
        	if(!st.hasMoreTokens())st=new StringTokenizer(br.readLine());
            for(int y=0;y<m;y++)ar[x][y]=Integer.parseInt(st.nextToken());
        }
        return ar;
    }
    static long[] arl(int n)throws IOException
    {
        long ar[]=new long[n];
        if(!st.hasMoreTokens())st=new StringTokenizer(br.readLine());
        for(int x=0;x<n;x++) ar[x]=Long.parseLong(st.nextToken());
        return ar;
    }
    static long[][] arl(int n,int m)throws IOException
    {
        long ar[][]=new long[n][m];
        for(int x=0;x<n;x++)
        {
        	if(!st.hasMoreTokens())st=new StringTokenizer(br.readLine());
            for(int y=0;y<m;y++)ar[x][y]=Long.parseLong(st.nextToken());
        }
        return ar;
    }
    static String[] ars(int n)throws IOException
    {
        String ar[]=new String[n];
        if(!st.hasMoreTokens())st=new StringTokenizer(br.readLine());
        for(int x=0;x<n;x++) ar[x]=st.nextToken();
        return ar;
    }
    static double[] ard(int n)throws IOException
    {
        double ar[]=new double[n];
        if(!st.hasMoreTokens())st=new StringTokenizer(br.readLine());
        for(int x=0;x<n;x++)ar[x]=Double.parseDouble(st.nextToken());
        return ar;
    }
    static double[][] ard(int n,int m)throws IOException
    {
        double ar[][]=new double[n][m];
        for(int x=0;x<n;x++)
        {
        	if(!st.hasMoreTokens())st=new StringTokenizer(br.readLine());
            for(int y=0;y<m;y++)ar[x][y]=Double.parseDouble(st.nextToken());
        }
        return ar;
    }
    static char[] arc(int n)throws IOException
    {
        char ar[]=new char[n];
        if(!st.hasMoreTokens())st=new StringTokenizer(br.readLine());
        for(int x=0;x<n;x++)ar[x]=st.nextToken().charAt(0);
        return ar;
    }
    static char[][] arc(int n,int m)throws IOException
    {
        char ar[][]=new char[n][m];
        for(int x=0;x<n;x++)
        {
            String s=br.readLine();
            for(int y=0;y<m;y++)ar[x][y]=s.charAt(y);
        }
        return ar;
    }
    static void p(int ar[])
    {
        StringBuilder sb=new StringBuilder(11*ar.length);
        for(int a:ar)
        {
        	sb.append(a);
        	sb.append(' ');
        }
        System.out.println(sb);
    }
    static void p(int ar[][])
    {
        StringBuilder sb;
        for(int a[]:ar)
        {
            sb=new StringBuilder(2*a.length);
            for(int aa:a)
            {
            	sb.append(aa);
            	sb.append(' ');
            }
            System.out.println(sb);
        }
    }
    static void p(long ar[])
    {
        StringBuilder sb=new StringBuilder(20*ar.length);
        for(long a:ar)
        {
        	sb.append(a);
        	sb.append(' ');
        }
        System.out.println(sb);
    }
    static void p(long ar[][])
    {
        StringBuilder sb;
        for(long a[]:ar)
        {
            sb=new StringBuilder(2*a.length);
            for(long aa:a)
            {
            	sb.append(aa);
            	sb.append(' ');
            }
            System.out.println(sb);
        }
    }
    static void p(String ar[])
    {
        StringBuilder sb=new StringBuilder(2*ar.length);
        for(String a:ar)
        {
        	sb.append(a);
        	sb.append(' ');
        }
        System.out.println(sb);
    }
    static void p(double ar[])
    {
        StringBuilder sb=new StringBuilder(20*ar.length);
        for(double a:ar)
        {
        	sb.append(a);
        	sb.append(' ');
        }
        System.out.println(sb);
    }
    static void p(double ar[][])
    {
        StringBuilder sb;
        for(double a[]:ar)
        {
            sb=new StringBuilder(4*a.length);
            for(double aa:a)
            {
            	sb.append(aa);
            	sb.append(' ');
            }
            System.out.println(sb);
        }
    }
    static void p(char ar[])
    {
        StringBuilder sb=new StringBuilder(2*ar.length);
        for(char aa:ar)
        {
        	sb.append(aa);
        	sb.append(' ');
        }
        System.out.println(sb);
    }
    static void p(char ar[][])
    {
        StringBuilder sb;
        for(char a[]:ar)
        {
            sb=new StringBuilder(2*a.length);
            for(char aa:a)
            {
            	sb.append(aa);
            	sb.append(' ');
            }
            System.out.println(sb);
        }
    }
}