Two pirates Polycarpus and Vasily play a very interesting game. They have n chests with coins, the chests are numbered with integers from 1 to n. Chest number i has ai coins. 

Polycarpus and Vasily move in turns. Polycarpus moves first. During a move a player is allowed to choose a positive integer x (2·x + 1 ≤ n) and take a coin from each chest with numbers x, 2·x, 2·x + 1. It may turn out that some chest has no coins, in this case the player doesn't take a coin from this chest. The game finishes when all chests get emptied.

Polycarpus isn't a greedy scrooge. Polycarpys is a lazy slob. So he wonders in what minimum number of moves the game can finish. Help Polycarpus, determine the minimum number of moves in which the game can finish. Note that Polycarpus counts not only his moves, he also counts Vasily's moves.

Input

The first line contains a single integer n (1 ≤ n ≤ 100) — the number of chests with coins. The second line contains a sequence of space-separated integers: a1, a2, ..., an (1 ≤ ai ≤ 1000), where ai is the number of coins in the chest number i at the beginning of the game.

Output

Print a single integer — the minimum number of moves needed to finish the game. If no sequence of turns leads to finishing the game, print -1.

Examples

Input

1
1


Output

-1


Input

3
1 2 3


Output

3

Note

In the first test case there isn't a single move that can be made. That's why the players won't be able to empty the chests.

In the second sample there is only one possible move x = 1. This move should be repeated at least 3 times to empty the third chest.
   // package com.company;
    import java.io.BufferedReader;
    import java.io.IOException;
    import java.io.InputStreamReader;
    import java.lang.reflect.Array;
    import java.util.*;
    public class Main {

        public static void main(String[] args) throws IOException {
           Scanner s = new Scanner(System.in);
       //     BufferedReader s=new BufferedReader(new InputStreamReader(System.in));
             StringBuilder sb = new StringBuilder();//int n=Integer.parseInt(s.readLine());
         int n=s.nextInt();
        int[] a=new int[n+1];
        for(int i=1;i<=n;i++){
        a[i]=s.nextInt();
        }long ans=0;int flag=0;
        for(int i=n;i>0;i--){
         if(i%2==0){
             if(a[i]>0){
                 if(i+1<=n&&i/2>0){ans+=a[i];
                 a[i/2]=Math.max(a[i/2]-a[i],0);
                    a[i+1]=Math.max(a[i+1]-a[i],0);

                 }else if(2*i+1<=n){ans+=a[i];
                    a[i*2]=Math.max(a[i*2]-a[i],0);
                    a[2*i+1]=Math.max(a[2*i+1]-a[i],0);

                 }else{
                 flag=1;break;}
             }
         }else{
            if(i/2>0){ ans+=a[i];
            a[i/2]=Math.max(a[i/2]-a[i],0);
        //    else if(a[i]>0)flag=1;
            a[i-1]=Math.max(a[i-1]-a[i],0);}
            else if(2*i+1<=n){ans+=a[i];
                a[i*2]=Math.max(a[i*2]-a[i],0);
                a[2*i+1]=Math.max(a[2*i+1]-a[i],0);

            }else{
                flag=1;break;}
         }
        }
        if(flag==1){
            System.out.println(-1);
        }else{
            System.out.println(ans);
        }
        }
        static boolean isPrime(int n)
        {
            // Corner cas
            if (n <= 1) return false;
            if (n <= 3) return true;

            // This is checked so that we can skip
            // middle five numbers in below loop
            if (n % 2 == 0 || n % 3 == 0) return false;

            for (int i = 5; i * i <= n; i = i + 6)
                if (n % i == 0 || n % (i + 2) == 0)
                    return false;

            return true;
        }
        static boolean isPrime(int n, int k)
        {
            // Corner cases
            if (n <= 1 || n == 4) return false;
            if (n <= 3) return true;

            // Try k times
            while (k > 0)
            {
                // Pick a random number in [2..n-2]
                // Above corner cases make sure that n > 4
                int a = 2 + (int)(Math.random() % (n - 4));

                // Fermat's little theorem
                if (power(a, n - 1, n) != 1)
                    return false;

                k--;
            }

            return true;
        }
        static double power(double x, long y, int p) {
            double res = 1;
            x = x % p;
            while (y > 0) {
                if ((y & 1) == 1)
                    res = (res * x) % p;
                y = y >> 1;
                x = (x * x) % p;
            }
            return res;
        }
        public static void fracion(double x) {
            String a = "" + x;
            String spilts[] = a.split("\\."); // split using decimal
            int b = spilts[1].length(); // find the decimal length
            int denominator = (int) Math.pow(10, b); // calculate the denominator
            int numerator = (int) (x * denominator); // calculate the nerumrator Ex
            // 1.2*10 = 12
            int gcd = gcd(numerator, denominator); // Find the greatest common
            // divisor bw them
            String fraction = "" + numerator / gcd + "/" + denominator / gcd;
            // System.out.println((denominator/gcd));
            long x1=modInverse(denominator / gcd,998244353  );
            //  System.out.println(x1);
            System.out.println((((numerator / gcd )%998244353 *(x1%998244353  ))%998244353  ) );
        }static int max=Integer.MIN_VALUE;
static int max1=Integer.MIN_VALUE;static int[] ans;static long[][] dp;static int[][] c;
        public static int dfs(int papa, int i, ArrayList<Integer>[] h, int[] vis) {

             vis[i] = 1;
               if(papa!=-1){
                   dp[i-1][0]=Math.min(dp[i-1][0],c[0][i-1]+Math.min(dp[papa-1][1],dp[papa-1][2]));
                   dp[i-1][1]=Math.min(dp[i-1][1],c[1][i-1]+Math.min(dp[papa-1][0],dp[papa-1][2]));
                   dp[i-1][2]=Math.min(dp[i-1][2],c[2][i-1]+Math.min(dp[papa-1][1],dp[papa-1][0]));

               }else{
                   dp[i-1][0]=c[i-1][0];
                   dp[i-1][1]=c[i-1][1];
                   dp[i-1][2]=c[i-1][2];

               }
             for(Integer j:h[i]){
                      if(vis[j]==0){
                          dfs(i,j,h,vis);
                      }
             }ans[i]+=1;if(ans[i]>max){
                 max=ans[i];max1=i;
            }
          return ans[i];
        }



        public static void bfs(int i, HashMap<Integer, Integer>[] h, int[] vis, int len, int papa) {
            Queue<Integer> q = new LinkedList<Integer>();
            q.add(i);

        }


        static int i(String a) {
            return Integer.parseInt(a);
        }

        static long l(String a) {
            return Long.parseLong(a);
        }

        static String[] inp() throws IOException {
            BufferedReader s = new BufferedReader(new InputStreamReader(System.in));
            return s.readLine().trim().split("\\s+");
        }


        static int gcd(int a, int b) {
            if (b == 0)
                return a;
            return gcd(b, a % b);
        }
        static long modInverse(int a, int m)
        {


            {
                // If a and m are relatively prime, then modulo inverse
                // is a^(m-2) mode m
                return (power(a, m - 2, m));
            }
        }

        // To compute x^y under modulo m
        static long power(int x, int y, int m)
        {
            if (y == 0)
                return 1;

            long p = power(x, y / 2, m) % m;
            p = (p * p) % m;

            if (y % 2 == 0)
                return p;
            else
                return (x * p) % m;
        }

        // Function to return gcd of a and b

    }
    class Student
    {
        Integer l;Integer r;

        public Student(Integer l, Integer r) {
            this.l = l;
            this.r = r;

        }
    // Constructor


        // Used to print student details in main()
        public String toString()
        {
            return this.l+" ";
        }
    }

    class Sortbyroll implements Comparator<Student>
    {
        // Used for sorting in ascending order of
        // roll number
        public int compare(Student a, Student b){
            return b.r-a.r;
        }
    }