using Lib;
using System;
using System.Collections.Generic;
using System.Diagnostics;
using System.Diagnostics.Contracts;
using System.IO;
using System.Linq;
using System.Runtime.CompilerServices;
using System.Text;
using static Lib.OutputLib;
public class Solver
{
    const bool MultiTestCase = false;
    void Solve()
    {
        int n = ri;
        var s = rs;
        ReadArray(out int[] a, n);

        var st = new Stack<int>();
        var p = new int[n + 1];
        st.Push(0);
        for (int i = 1, k = 0; k < s.Length; k++)
        {
            if (s[k] == '(')
            {
                p[i] = st.Peek();
                st.Push(i++);
            }
            else
            {
                st.Pop();
            }
        }

        var graph = new UnweightedGraph(n + 1);
        for (int i = 1; i <= n; i++) graph.AddEdge(i, p[i]);
        var a0 = new long[n + 1];
        for (int i = 0; i < n; i++) a0[i + 1] = a[i];
        var b0 = new long[n + 1];
        Array.Fill(b0, 1);
        long ans = TreeWith01.Inversion(graph.ToArray(), a0, b0);
        Write(ans);
    }

#pragma warning disable CS0162, CS8618
    public Solver() { if (!MultiTestCase) Solve(); else for (int t = ri; t > 0; t--) Solve(); }
#pragma warning restore CS0162, CS8618

    const int IINF = 1 << 30;
    const long INF = 1L << 60;
    int ri { [MethodImpl(256)] get => (int)sc.Integer(); }
    long rl { [MethodImpl(256)] get => sc.Integer(); }
    uint rui { [MethodImpl(256)] get => (uint)sc.UInteger(); }
    ulong rul { [MethodImpl(256)] get => sc.UInteger(); }
    double rd { [MethodImpl(256)] get => sc.Double(); }
    string rs { [MethodImpl(256)] get => sc.Scan(); }
    string rline { [MethodImpl(256)] get => sc.Line(); }
    public StreamScanner sc = new StreamScanner(Console.OpenStandardInput());
    void ReadArray(out int[] a, int n) { a = new int[n]; for (int i = 0; i < a.Length; i++) a[i] = ri; }
    void ReadArray(out long[] a, int n) { a = new long[n]; for (int i = 0; i < a.Length; i++) a[i] = rl; }
    void ReadArray<T>(out T[] a, int n, Func<T> read) { a = new T[n]; for (int i = 0; i < a.Length; i++) a[i] = read(); }
    void ReadArray<T>(out T[] a, int n, Func<int, T> read) { a = new T[n]; for (int i = 0; i < a.Length; i++) a[i] = read(i); }
}

static class Program
{
    static public void Main(string[] args)
    {
        SourceExpander.Expander.Expand();
        Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false });
        new Solver();
        Console.Out.Flush();
    }
}
#region Expanded by https://github.com/kzrnm/SourceExpander
public class SimpleIntStack{int[]data;int index;public SimpleIntStack(int size_max){data=new int[size_max];index=0;}public int Count{get=>index;}public void Push(int value)=>data[index++]=value;public int Peek()=>data[index-1];public int Pop()=>data[ --index];public void Clear()=>index=0;}public class SimpleIntPairStack{(int,int)[]data;int index;public SimpleIntPairStack(int size_max){data=new(int,int)[size_max];index=0;}public int Count{get=>index;}public void Push((int,int)value)=>data[index++]=value;public void Push(int item1,int item2)=>data[index++]=(item1,item2);public(int,int)Peek()=>data[index-1];public(int,int)Pop()=>data[ --index];public void Clear()=>index=0;}
namespace Lib{public class UnionFind{internal int n;internal int[]p;public int GroupCount{get;internal set;}public UnionFind(int _n){n=_n;GroupCount=n;p=Enumerable.Repeat(-1,n).ToArray();}public void Clear(){Array.Fill(p,-1);}public int Root(int x){if(p[x]<0)return x;return p[x]=Root(p[x]);}public int Size(int x)=>-p[Root(x)];public bool IsSame(int x,int y)=>Root(x)==Root(y);public bool Unite(int x,int y){x=Root(x);y=Root(y);if(x==y)return false;if(-p[x]<-p[y])(x,y)=(y,x);p[x]+=p[y];p[y]=x;GroupCount--;return true;}public int[][]GetGroups(){var leader_buf=new int[n];var group_size=new int[n];int group_count=0;for(int i=0;i<n;i++){leader_buf[i]=Root(i);if(leader_buf[i]==i)group_count++;group_size[leader_buf[i]]++;}var result=new int[n][];for(int i=0;i<n;i++)result[i]=new int[group_size[i]];var idx=new int[n];for(int i=0;i<n;i++)result[leader_buf[i]][idx[leader_buf[i]]++]=i;var res=new int[group_count][];for(int i=0,j=0;i<n;i++)if(leader_buf[i]==i)res[j++]=result[i];return res;}}}
namespace Lib{public class Graph<T>{public struct Edge{public int from,to;public T data;public Edge(int _from,int _to,T _data){from=_from;to=_to;data=_data;}public Edge(int _to,T _data){from=-1;to=_to;data=_data;}}int n;public int Size=>n;public List<Edge>[]edges;public Graph(Graph<T>_g){n=_g.Size;edges=new List<Edge>[n];for(int i=0;i<n;i++)edges[i]=new List<Edge>(_g.edges[i]);}public Graph(List<int>[]_g,Func<T>_e){n=_g.Length;edges=new List<Edge>[n];for(int i=0;i<n;i++)edges[i]=new List<Edge>();for(int i=0;i<n;i++)foreach(var j in _g[i])edges[i].Add(new Edge(i,j,_e()));}public Graph(int[][]_g,Func<T>_e){n=_g.Length;edges=new List<Edge>[n];for(int i=0;i<n;i++)edges[i]=new List<Edge>();for(int i=0;i<n;i++)foreach(var j in _g[i])edges[i].Add(new Edge(i,j,_e()));}public Graph(int _n){n=_n;edges=new List<Edge>[n];for(int i=0;i<n;i++)edges[i]=new List<Edge>();}public void AddEdge(int x,int y,T data){edges[x].Add(new Edge(x,y,data));edges[y].Add(new Edge(y,x,data));}public void AddDirectedEdge(int src,int to,T data){edges[src].Add(new Edge(src,to,data));}public Edge[][]ToArray(bool sort=true){if(sort)for(int i=0;i<n;i++)edges[i].Sort((e,f)=>e.to.CompareTo(f.to));var g=new Edge[n][];for(int i=0;i<n;i++)g[i]=edges[i].ToArray();return g;}public int[][]ToUnweightedArray(bool sort=true){if(sort)for(int i=0;i<n;i++)edges[i].Sort((e,f)=>e.to.CompareTo(f.to));var g=new int[n][];for(int i=0;i<n;i++)g[i]=edges[i].Select(e=>e.to).ToArray();return g;}public(Edge[]csr,int[]start)ToCSR(bool sort=true){if(sort)for(int i=0;i<n;i++)edges[i].Sort((e,f)=>e.to.CompareTo(f.to));var start=new int[n+1];for(int i=0;i<n;i++)start[i+1]=start[i]+edges[i].Count;var csr=new Edge[start[n]];for(int i=0;i<n;i++)for(int j=0;j<edges[i].Count;j++)csr[j+start[i]]=edges[i][j];return(csr,start);}public(int[]csr,int[]csr_start)ToUnweightedCSR(bool sort=true){if(sort)for(int i=0;i<n;i++)edges[i].Sort((e,f)=>e.to.CompareTo(f.to));var start=new int[n+1];for(int i=0;i<n;i++)start[i+1]=start[i]+edges[i].Count;var csr=new int[start[n]];for(int i=0;i<n;i++)for(int j=0;j<edges[i].Count;j++)csr[j+start[i]]=edges[i][j].to;return(csr,start);}}}
namespace Lib{public class UnweightedGraph:Graph<int>{public UnweightedGraph(UnweightedGraph _g):base(_g){}public UnweightedGraph(List<int>[]_g):base(_g,()=>1){}public UnweightedGraph(int _n):base(_n){}[MethodImpl(256)]public void AddEdge(int x,int y)=>AddEdge(x,y,1);[MethodImpl(256)]public void AddDirectedEdge(int src,int to)=>AddDirectedEdge(src,to,1);public new int[][]ToArray(bool sort=true)=>ToUnweightedArray(sort);public new(int[]csr,int[]csr_start)ToCSR(bool sort=true)=>ToUnweightedCSR(sort);}}
namespace Lib{public partial class StreamScanner{public StreamScanner(Stream stream){str=stream;}private readonly Stream str;private readonly byte[]buf=new byte[1024];private int len,ptr;public bool isEof=false;public bool IsEndOfStream{get{return isEof;}}[MethodImpl(256)]private byte Read(){if(isEof)throw new EndOfStreamException();if(ptr>=len){ptr=0;if((len=str.Read(buf,0,1024))<=0){isEof=true;return 0;}}return buf[ptr++];}[MethodImpl(256)]public char Char(){byte b;do b=Read();while(b<33||126<b);return(char)b;}[MethodImpl(256)]public string Line(){var sb=new StringBuilder();for(var b=Char();b!=10&&!isEof;b=(char)Read())sb.Append(b);return sb.ToString();}[MethodImpl(256)]public string Scan(){var sb=new StringBuilder();for(var b=Char();b>=33&&b<=126;b=(char)Read())sb.Append(b);return sb.ToString();}[MethodImpl(256)]public long Integer(){long ret=0;var ng=false;byte b;do b=Read();while(b!='-'&&(b<'0'||'9'<b));if(b=='-'){ng=true;b=Read();}for(;'0'<=b&&b<='9';b=Read())ret=ret*10+(b^'0');return ng?-ret:ret;}[MethodImpl(256)]public ulong UInteger(){ulong ret=0;byte b;do b=Read();while(b<'0'||'9'<b);for(;'0'<=b&&b<='9';b=Read())ret=ret*10+(ulong)(b^'0');return ret;}[MethodImpl(256)]public double Double()=>double.Parse(Scan());}}
namespace Lib{public static class OutputLib{[MethodImpl(256)]public static void WriteJoin<T>(string s,IEnumerable<T>t)=>Console.WriteLine(string.Join(s,t));[MethodImpl(256)]public static void WriteMat<T>(T[,]a,string sep=" "){int sz1=a.GetLength(0),sz2=a.GetLength(1);var b=new T[sz2];for(int i=0;i<sz1;i++){for(int j=0;j<sz2;j++)b[j]=a[i,j];WriteJoin(sep,b);}}[MethodImpl(256)]public static void WriteMat<T>(T[][]a,string sep=" "){foreach(var ar in a)WriteJoin(sep,ar);}[MethodImpl(256)]public static void WriteMat<T>(T[][]a,Func<T,string>map,string sep=" "){foreach(var ar in a)WriteJoin(sep,ar.Select(x=>map(x)));}[MethodImpl(256)]public static void Write(object t)=>Console.WriteLine(t.ToString());[MethodImpl(256)]public static void Write(params object[]arg)=>Console.WriteLine(string.Join(" ",arg.Select(x=>x.ToString())));[MethodImpl(256)]public static void Write(string str)=>Console.WriteLine(str);[MethodImpl(256)]public static void WriteFlush(object t){Console.WriteLine(t.ToString());Console.Out.Flush();}[MethodImpl(256)]public static void WriteError(object t)=>Console.Error.WriteLine(t.ToString());[MethodImpl(256)]public static void Flush()=>Console.Out.Flush();[MethodImpl(256)]public static void YN(bool t)=>Console.WriteLine(t?"YES":"NO");[MethodImpl(256)]public static void Yn(bool t)=>Console.WriteLine(t?"Yes":"No");[MethodImpl(256)]public static void yn(bool t)=>Console.WriteLine(t?"yes":"no");[MethodImpl(256)]public static void DeleteLine()=>Console.Write("\x1b[1A\x1b[2K");[MethodImpl(256)]public static void ProgressBar(long now,long total,int blocks=50){int x=(int)((2*now*blocks+1)/(2*total));Console.Write($"\x1b[G[\x1b[42m{string.Concat(Enumerable.Repeat("_",x))}\x1b[0m{string.Concat(Enumerable.Repeat("_",blocks-x))}] : {now} / {total}");}}}
namespace Lib{public static class TreeWith01{struct F:IComparable<F>{public long a{get;private set;}public long b{get;private set;}public F(long a,long b){this.a=a;this.b=b;}public int CompareTo(F x)=>(a*x.b).CompareTo(b*x.a);}public static long Inversion(in int[][]g,ReadOnlySpan<long>a0,ReadOnlySpan<long>b0,int root=0){var a=a0.ToArray();var b=b0.ToArray();if(a.Min()>=0){int n=g.Length;var seen=new bool[n];seen[root]=true;var p=new int[n];p[root]=-1;var st=new SimpleIntStack(n);st.Push(root);while(st.Count>0){int x=st.Pop();foreach(var y in g[x])if(y!=p[x]){p[y]=x;st.Push(y);}}var pq=new PriorityQueue<(int v,long a,long b),F>();for(int i=0;i<n;i++)if(!seen[i])pq.Enqueue((i,a[i],b[i]),new F(b[i],a[i]));var uf=new UnionFind(n);long ans=0;while(pq.Count>0){var(v,_a,_b)=pq.Dequeue();if(v!=uf.Root(v))continue;if(a[v]!=_a||b[v]!=_b||seen[v])continue;int u=uf.Root(p[v]);ans+=b[u]*a[v];uf.Unite(u,v);int w=uf.Root(u);seen[u]=true;seen[v]=true;seen[w]=false;p[w]=p[u];a[w]=a[u]+a[v];b[w]=b[u]+b[v];if(p[w]!=-1)pq.Enqueue((w,a[w],b[w]),new F(b[w],a[w]));}return ans;}else if(b.Min()>=0){int n=g.Length;var seen=new bool[n];seen[root]=true;var p=new int[n];p[root]=-1;var st=new SimpleIntStack(n);st.Push(root);while(st.Count>0){int x=st.Pop();foreach(var y in g[x])if(y!=p[x]){p[y]=x;st.Push(y);}}var pq=new PriorityQueue<(int v,long a,long b),F>();for(int i=0;i<n;i++)if(!seen[i])pq.Enqueue((i,a[i],b[i]),new F(-a[i],b[i]));var uf=new UnionFind(n);long ans=0;while(pq.Count>0){var(v,_a,_b)=pq.Dequeue();if(v!=uf.Root(v))continue;if(a[v]!=_a||b[v]!=_b||seen[v])continue;int u=uf.Root(p[v]);ans+=b[u]*a[v];uf.Unite(u,v);int w=uf.Root(u);seen[u]=true;seen[v]=true;seen[w]=false;p[w]=p[u];a[w]=a[u]+a[v];b[w]=b[u]+b[v];if(p[w]!=-1)pq.Enqueue((w,a[w],b[w]),new F(-a[w],b[w]));}return ans;}else Contract.Assert(false);return-1;}}}
namespace SourceExpander{public class Expander{[Conditional("EXP")]public static void Expand(string inputFilePath=null,string outputFilePath=null,bool ignoreAnyError=true){}public static string ExpandString(string inputFilePath=null,bool ignoreAnyError=true){return "";}}}
#endregion Expanded by https://github.com/kzrnm/SourceExpander