Vasiliy is fond of solving different tasks. Today he found one he wasn't able to solve himself, so he asks you to help.

Vasiliy is given n strings consisting of lowercase English letters. He wants them to be sorted in lexicographical order (as in the dictionary), but he is not allowed to swap any of them. The only operation he is allowed to do is to reverse any of them (first character becomes last, second becomes one before last and so on).

To reverse the i-th string Vasiliy has to spent ci units of energy. He is interested in the minimum amount of energy he has to spent in order to have strings sorted in lexicographical order.

String A is lexicographically smaller than string B if it is shorter than B (|A| < |B|) and is its prefix, or if none of them is a prefix of the other and at the first position where they differ character in A is smaller than the character in B.

For the purpose of this problem, two equal strings nearby do not break the condition of sequence being sorted lexicographically.

Input

The first line of the input contains a single integer n (2 ≤ n ≤ 100 000) — the number of strings.

The second line contains n integers ci (0 ≤ ci ≤ 109), the i-th of them is equal to the amount of energy Vasiliy has to spent in order to reverse the i-th string. 

Then follow n lines, each containing a string consisting of lowercase English letters. The total length of these strings doesn't exceed 100 000.

Output

If it is impossible to reverse some of the strings such that they will be located in lexicographical order, print  - 1. Otherwise, print the minimum total amount of energy Vasiliy has to spent.

Examples

Input

2
1 2
ba
ac


Output

1


Input

3
1 3 1
aa
ba
ac


Output

1


Input

2
5 5
bbb
aaa


Output

-1


Input

2
3 3
aaa
aa


Output

-1

Note

In the second sample one has to reverse string 2 or string 3. To amount of energy required to reverse the string 3 is smaller.

In the third sample, both strings do not change after reverse and they go in the wrong order, so the answer is  - 1.

In the fourth sample, both strings consists of characters 'a' only, but in the sorted order string "aa" should go before string "aaa", thus the answer is  - 1.
import java.io.*;
import java.lang.reflect.Array;
import java.math.BigInteger;
import java.util.*;
import java.lang.*;
import static java.lang.Math.*;
public class main implements Runnable {

    public static void main(String[] args) {
        new Thread(null, new main(), "Check2", 1 << 28).start();// to increse stack size in java
    }
    void init(ArrayList <Integer> adj[], int n){
        for(int i=0;i<=n;i++)adj[i]=new ArrayList<>();
    }
    static long mod = (long) (1e9 + 7);
    public void run() {
        InputReader in = new InputReader(System.in);
        PrintWriter w = new PrintWriter(System.out);

        int n=in.nextInt();
        cost=new long[n];
        s=new String[n];
        dp=new long[n][2];
        for(int i=0;i<n;i++)for(int j=0;j<2;j++)dp[i][j]=-1;
        for(int i=0;i<n;i++)cost[i]=in.nextLong();

        for(int i=0;i<n;i++){
            s[i]=in.next();
        }

        long val=rec(0,n,"",0);
        if(val!=Long.MAX_VALUE)w.println(val);
        else
            w.println(-1);




        w.close();
    }
    long cost[],dp[][];                 // o for not ,1 for rev
    String s[];
    long rec(int i,int n,String prv,int last){
        if(i==n)return 0;

        if(dp[i][last]!=-1)return dp[i][last];
        long ans1=Long.MAX_VALUE;
        long ans2=Long.MAX_VALUE;
        char d[]=new char[s[i].length()];
        for(int j=0;j<d.length;j++){
            d[j]=s[i].charAt(d.length-j-1);
        }
        String nn=String.valueOf(d);
        if(prv.equals("")||s[i].compareTo(prv)>=0)
        ans1=rec(i+1,n,s[i],0);
        if(prv.equals("")||nn.compareTo(prv)>=0)
        ans2=rec(i+1,n,nn,1);

        if(ans2!=Long.MAX_VALUE){
            ans2+=cost[i];
        }
        return dp[i][last]=min(ans1,ans2);
    }



    static void diji(int s, long dist[], ArrayList<pair> adj[]) {
        dist[s] = 0;
        PriorityQueue<pair> q = new PriorityQueue<>(new cmp());
        q.add(new pair(s, 0));
        while (!q.isEmpty()) {
            pair p1 = q.poll();
            for (pair ne: adj[p1.a]) {

                if ((long) p1.b + (long) ne.b < dist[ne.a]) {
                    dist[ne.a] = (long) p1.b + (long) ne.b;
                    pair p2 = new pair(ne.a, dist[ne.a]);
                    q.add(p2);

                }

            }
        }

    }
    static class cmp implements Comparator<pair>{

        public  int compare(pair o1,pair o2)
        {
            return o1.b<o2.b?-1:o1.b>o2.b?1:0;
        }

    }

    static class pair {
        int a;
        long b;
        pair(int a,long b){
            this.a=a;
            this.b=b;
        }
        public boolean equals(Object obj) {      //  override equals method for object to remove tem from arraylist and sets etc.......
            if (this == obj)
                return true;
            if (obj == null)
                return false;
            if (getClass() != obj.getClass())
                return false;
            pair other = (pair) obj;
            if (b!= other.b||a!=other.a)
                return false;
            return true;
        }
    }

    static long modinv(long a,long b)
    {
        long p=power(b,mod-2);

        p=a%mod*p%mod;
        p%=mod;

        return p;

    }

    static long power(long x,long y){
        if(y==0)return 1%mod;
        if(y==1)return x%mod;


        long res=1;
        x=x%mod;
        while(y>0){


            if((y%2)!=0){
                res=(res*x)%mod;
            }


            y=y/2;
            x=(x*x)%mod;
        }


        return res;

    }
    static  long gcd(long a,long b){

        if(b==0)return a;
        return gcd(b,a%b);
    }

    static  void sev(int a[],int n){

        for(int i=2;i<=n;i++)a[i]=i;
        for(int i=2;i<=n;i++){

            if(a[i]!=0){
                for(int j=2*i;j<=n;){

                    a[j]=0;
                    j=j+i;
                }
            }

        }

    }



    static class InputReader
    {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private SpaceCharFilter filter;

        public InputReader(InputStream stream)
        {
            this.stream = stream;
        }

        public int read()
        {
            if (numChars==-1)
                throw new InputMismatchException();

            if (curChar >= numChars)
            {
                curChar = 0;
                try
                {
                    numChars = stream.read(buf);
                }
                catch (IOException e)
                {
                    throw new InputMismatchException();
                }

                if(numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public String nextLine()
        {
            BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
        public int nextInt()
        {
            int c = read();

            while(isSpaceChar(c))
                c = read();

            int sgn = 1;

            if (c == '-')
            {
                sgn = -1;
                c = read();
            }

            int res = 0;
            do
            {
                if(c<'0'||c>'9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c));

            return res * sgn;
        }

        public long nextLong()
        {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-')
            {
                sgn = -1;
                c = read();
            }
            long res = 0;

            do
            {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c));
            return res * sgn;
        }

        public double nextDouble()
        {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-')
            {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.')
            {
                if (c == 'e' || c == 'E')
                    return res * Math.pow(10, nextInt());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.')
            {
                c = read();
                double m = 1;
                while (!isSpaceChar(c))
                {
                    if (c == 'e' || c == 'E')
                        return res * Math.pow(10, nextInt());
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }

        public String readString()
        {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do
            {
                res.appendCodePoint(c);
                c = read();
            }
            while (!isSpaceChar(c));

            return res.toString();
        }

        public boolean isSpaceChar(int c)
        {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public String next()
        {
            return readString();
        }

        public interface SpaceCharFilter
        {
            public boolean isSpaceChar(int ch);
        }
    }







}
