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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.*;
import java.util.function.Function;

public class Main {

    public static void main(String[] args) {

        Parser parser = new Parser();
        int t = 1;
        for (int i = 1; i <= t; i++) {
            Problem problem = new Problem();
            problem.solve(i);
        }
    }
}

class Problem {
    Parser parser = new Parser();

    int n;
    char[] arr;
    int[] a = new int[n];
    long[][][] dp;

    public void solve(int testNum) {
        n = parser.parseInt();
        arr = parser.parseString().toCharArray();

        a = new int[n + 9];
        for(int i = 1; i <= n; i++) {
            a[i] = parser.parseInt();
        }

        dp = new long[n + 9][n + 9][n + 9];
        for(int i = 0; i <= n; i++) {
            for(int j = 0; j <= n; j++) {
                Arrays.fill(dp[i][j], -1);
            }
        }

        System.out.println(get(0, n, 1));
    }

    long get(int l, int r, int c) {

        if(l >= r) {
            return 0;
        }

        if(dp[l][r][c] != -1) {
            return dp[l][r][c];
        }

        long res = a[c] + get(l + 1, r, 1);
        for(int i = l + 1; i < r; i++) {
            if(arr[l] == arr[i]) {
                res = Math.max(res, get(l + 1, i, 1) + get(i, r, c + 1));
            }
        }

        return dp[l][r][c] = res;
    }
}

class MathUtil {

    public static List<Integer> getPrimes(int r) {
        if (r < 2) {
            return List.of();
        }

        List<Integer> result = new ArrayList<>();
        result.add(2);
        boolean[] is = new boolean[r + 1];
        for (int i = 4; i <= r; i += 2) {
            is[i] = true;
        }
        for (int i = 3; i <= r; i += 2) {
            if (is[i]) continue;
            result.add(i);
            for (long j = (long) i * i; j <= r; j += i) {
                is[(int) j] = true;
            }
        }
        return result;
    }

    public static long gcd(long a, long b) {
        return b == 0 ? a : gcd(b, a % b);
    }

    public static long pow(long x, long y) {
        return pow(x, y, Function.identity());
    }

    public static long pow(long x, long y, long mod) {
        return pow(x, y, v -> v % mod);
    }

    private static long pow(long x, long y, Function<Long, Long> action) {
        long res = 1;
        long t = x;
        while (y > 0) {
            if ((y & 1) == 1) {
                res *= t;
                res = action.apply(res);
            }
            t *= t;
            t = action.apply(t);
            y /= 2;
        }
        return res;
    }
}

class DisjointSet {

    private final int[] f;

    public DisjointSet(int size) {
        f = new int[size + 1];
        for (int i = 0; i <= size; i++) {
            f[i] = i;
        }
    }

    public int find(int u) {
        if (f[u] == u) return u;
        return f[u] = find(f[u]);
    }

    public boolean merge(int u, int v) {
        u = find(u);
        v = find(v);
        if (u == v) return false;
        if (u > v) {
            int t = u;
            u = v;
            v = t;
        }
        f[u] = v;
        return true;
    }
}

class Parser {
    private static final BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
    private StringTokenizer tokenizer;

    public int parseInt() {
        fill();
        return Integer.parseInt(tokenizer.nextToken());
    }

    public long parseLong() {
        fill();
        return Long.parseLong(tokenizer.nextToken());
    }

    public double parseDouble() {
        fill();
        return Double.parseDouble(tokenizer.nextToken());
    }

    public String parseLine() {
        try {
            return reader.readLine();
        } catch (IOException e) {
            e.printStackTrace();
        }
        return null;
    }

    String parseString() {
        fill();
        return tokenizer.nextToken();
    }

    private void fill() {
        while (tokenizer == null || !tokenizer.hasMoreElements()) {
            try {
                tokenizer = new StringTokenizer(reader.readLine());
            } catch (IOException e) {
                e.printStackTrace();
            }
        }
    }
}