Vasya has a string s of length n consisting only of digits 0 and 1. Also he has an array a of length n. 

Vasya performs the following operation until the string becomes empty: choose some consecutive substring of equal characters, erase it from the string and glue together the remaining parts (any of them can be empty). For example, if he erases substring 111 from string 111110 he will get the string 110. Vasya gets a_x points for erasing substring of length x.

Vasya wants to maximize his total points, so help him with this! 

Input

The first line contains one integer n (1 ≤ n ≤ 100) — the length of string s.

The second line contains string s, consisting only of digits 0 and 1.

The third line contains n integers a_1, a_2, ... a_n (1 ≤ a_i ≤ 10^9), where a_i is the number of points for erasing the substring of length i.

Output

Print one integer — the maximum total points Vasya can get.

Examples

Input


7
1101001
3 4 9 100 1 2 3


Output


109


Input


5
10101
3 10 15 15 15


Output


23

Note

In the first example the optimal sequence of erasings is: 1101001 → 111001 → 11101 → 1111 → ∅.

In the second example the optimal sequence of erasings is: 10101 → 1001 → 11 → ∅.
import java.lang.*;
import java.math.*;
import java.util.*;
import java.io.*;
public class Main {
    void solve(){
        int n=ni();
        char s[]=ns().toCharArray();
        long dp[][][][]=new long[n+1][n+1][2][n+1];
        long dp2[]=new long[n+1];
        long a[]=new long[n+1];
        long ans[][]=new long[n+1][n+1];
        long pref[][]=new long[n+1][2];
        for(int i=1;i<=n;i++){
            a[i]=nl();
            pref[i][0]=pref[i-1][0];
            pref[i][1]=pref[i-1][1];
            pref[i][s[i-1]-'0']++;
        }
        for(int i=1;i<=n;i++){
            for(int x=1;x<=i;x++){
                dp2[i]=Math.max(dp2[i],a[x]+dp2[i-x]);

            }
        }
        for(int i=1;i<=n;i++) for(int j=1;j<=n;j++) {
            Arrays.fill(dp[i][j][0],-1);
            Arrays.fill(dp[i][j][1],-1);
        }
        for(int i=1;i<=n;i++){
            dp[i][i][0][0]=dp[i][i][1][0]=a[1];
            dp[i][i][s[i-1]-'0'][1]=0;
            ans[i][i]=a[1];
        }

        for(int len=2;len<=n;len++){
            for(int i=1;i<=n-len+1;i++){
                int j=i+len-1;
                for(int x=1;x<=pref[j][s[i-1]-'0']-pref[i-1][s[i-1]-'0'];x++){
                    if(x==1){
                        dp[i][j][s[i-1]-'0'][1]=ans[i+1][j];
                        ans[i][j]=Math.max(ans[i][j],dp[i][j][s[i-1]-'0'][1]+a[1]);
                        continue;
                    }
                    for(int k=i+1;k<=j;k++){
                        if(s[k-1]!=s[i-1]) continue;
                        if(i+1<=k-1) {
                          if(dp[k][j][s[i - 1] - '0'][x - 1] !=-1)   dp[i][j][s[i - 1] - '0'][x] = Math.max(dp[i][j][s[i - 1] - '0'][x], dp[k][j][s[i - 1] - '0'][x - 1] + ans[i + 1][k - 1]);
                        }
                        else  if(dp[k][j][s[i - 1] - '0'][x - 1] !=-1)dp[i][j][s[i-1]-'0'][x]=Math.max(dp[i][j][s[i-1]-'0'][x],dp[k][j][s[i-1]-'0'][x-1]);
                    }
                    if(dp[i][j][s[i-1]-'0'][x]!=-1)
                 ans[i][j]=Math.max(ans[i][j],dp[i][j][s[i-1]-'0'][x]+dp2[x]);
                }

            }
        }
        pw.println(ans[1][n]);


    }

    long M= (long)1e9+7;
    InputStream is;
    PrintWriter pw;
    String INPUT = "";
    void run() throws Exception {
        is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
        pw = new PrintWriter(System.out);
        long s = System.currentTimeMillis();
        solve();
        pw.flush();
        if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms");

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

    private byte[] inbuf = new byte[1024];
    public int lenbuf = 0, ptrbuf = 0;

    private int readByte() {
        if(lenbuf == -1)throw new InputMismatchException();
        if(ptrbuf >= lenbuf){
            ptrbuf = 0;
            try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
            if(lenbuf <= 0)return -1;
        }
        return inbuf[ptrbuf++];
    }

    private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
    private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }

    private double nd() { return Double.parseDouble(ns()); }
    private char nc() { return (char)skip(); }

    private String ns() {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }

    private char[] ns(int n) {
        char[] buf = new char[n];
        int b = skip(), p = 0;
        while(p < n && !(isSpaceChar(b))){
            buf[p++] = (char)b;
            b = readByte();
        }
        return n == p ? buf : Arrays.copyOf(buf, p);
    }

    private char[][] nm(int n, int m) {
        char[][] map = new char[n][];
        for(int i = 0;i < n;i++)map[i] = ns(m);
        return map;
    }

    private int[] na(int n) {
        int[] a = new int[n];
        for(int i = 0;i < n;i++)a[i] = ni();
        return a;
    }

    private int ni() {
        int num = 0, b;
        boolean minus = false;
        while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if(b == '-'){
            minus = true;
            b = readByte();
        }

        while(true){
            if(b >= '0' && b <= '9'){
                num = num * 10 + (b - '0');
            }else{
                return minus ? -num : num;
            }
            b = readByte();
        }
    }

    private long nl() {
        long num = 0;
        int b;
        boolean minus = false;
        while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if(b == '-'){
            minus = true;
            b = readByte();
        }

        while(true){
            if(b >= '0' && b <= '9'){
                num = num * 10 + (b - '0');
            }else{
                return minus ? -num : num;
            }
            b = readByte();
        }
    }
    private boolean oj = System.getProperty("ONLINE_JUDGE") != null;
    private void tr(Object... o) { if(INPUT.length() > 0)System.out.println(Arrays.deepToString(o)); }

}