Problem: You are given a string t and n strings s_1, s_2, ..., s_n. All strings consist of lowercase Latin letters.

Let f(t, s) be the number of occurences of string s in string t. For example, f('aaabacaa', 'aa') = 3, and f('ababa', 'aba') = 2.

Calculate the value of ∑_{i=1}^{n} ∑_{j=1}^{n} f(t, s_i + s_j), where s + t is the concatenation of strings s and t. Note that if there are two pairs i_1, j_1 and i_2, j_2 such that s_{i_1} + s_{j_1} = s_{i_2} + s_{j_2}, you should include both f(t, s_{i_1} + s_{j_1}) and f(t, s_{i_2} + s_{j_2}) in answer.

Input

The first line contains string t (1 ≤ |t| ≤ 2 ⋅ 10^5).

The second line contains integer n (1 ≤ n ≤ 2 ⋅ 10^5).

Each of next n lines contains string s_i (1 ≤ |s_i| ≤ 2 ⋅ 10^5).

It is guaranteed that ∑_{i=1}^{n} |s_i| ≤ 2 ⋅ 10^5. All strings consist of lowercase English letters.

Output

Print one integer — the value of ∑_{i=1}^{n} ∑_{j=1}^{n} f(t, s_i + s_j).

Examples

Input


aaabacaa
2
a
aa


Output


5


Input


aaabacaa
4
a
a
a
b


Output


33

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;
import java.text.*;

public class Main {
    //SOLUTION BEGIN
    //Into the Hardware Mode
    void pre() throws Exception{}
    void solve(int TC) throws Exception{
        String text = n();
        int N = ni();
        AhoCorasick aho1 = new AhoCorasick(), aho2 = new AhoCorasick();
        for(int i = 0; i< N; i++){
            String pat = n();
            aho1.addString(pat);
            aho2.addString(new StringBuilder(pat).reverse().toString());
        }
        aho1.buildSuffixLinks();
        aho2.buildSuffixLinks();

        int[] hit1 = aho1.count(text);
        text = new StringBuilder(text).reverse().toString();
        int[] hit2 = aho2.count(text);
        long ans = 0;
        int M = text.length();
        for(int i = 0; i< M-1; i++)ans += hit1[i]*(long)hit2[M-1-(i+1)];
        pn(ans);
    }
    public class AhoCorasick {
        State root, sentinal;
        int ID = 0;
        class State{
            TreeMap<Character, State> nxt;
            State suffixLink;
            char pch;
            boolean end;
            int hits, id;
            public State(char ch, int id){
                nxt = new TreeMap<>();
                end = false;this.id = id;
                pch = ch;hits = 0;
                suffixLink = null;
            }
            State nxt(Character ch){return nxt.get(ch);}
            void put(Character ch, State st){ nxt.put(ch, st);}
        }
        public AhoCorasick(){
            root = new State('$', ID++);
            sentinal = new State(' ', ID++);
            root.suffixLink = sentinal;
            for(char ch = 'a'; ch <= 'z'; ch++)sentinal.put(ch, root);
        }
        State addString(String s){
            State node = root;
            for(int i = 0; i< s.length(); i++){
                State nxt = node.nxt(s.charAt(i));
                if(nxt == null){
                    nxt = new State(s.charAt(i), ID++);
                    node.put(s.charAt(i), nxt);
                }
                node = nxt;
            }
            node.end = true;
            node.hits++;
            return node;
        }
        int[] count(String text){
            State node = root;
            int[] cnt = new int[text.length()];
            for(int i = 0; i< text.length(); i++){
                node = next(node, text.charAt(i));
                cnt[i] = node.hits;
            }
            return cnt;
        }
        State next(State st, char ch){
            State nxt;
            while((nxt = st.nxt(ch)) == null)st = st.suffixLink;
            return nxt;
        }
        void buildSuffixLinks(){
            Queue<State> q = new ArrayDeque<>();
            q.add(root);
            while(!q.isEmpty()){
                State st = q.poll();
                for(State nxt:st.nxt.values()){
                    nxt.suffixLink = next(st.suffixLink, nxt.pch);
                    nxt.hits += nxt.suffixLink.hits;
                    q.add(nxt);
                }
            }
        }
    }

    //SOLUTION END
    void hold(boolean b)throws Exception{if(!b)throw new Exception("Hold right there, Sparky!");}
    void exit(boolean b){if(!b)System.exit(0);}
    static void dbg(Object... o){System.err.println(Arrays.deepToString(o));}
    final long IINF = (long)2e18;
    final int INF = (int)1e9+2;
    DecimalFormat df = new DecimalFormat("0.00000000000");
    double PI = 3.141592653589793238462643383279502884197169399, eps = 1e-8;
    static boolean multipleTC = false, memory = true, fileIO = false;
    FastReader in;PrintWriter out;
    void run() throws Exception{
        long ct = System.currentTimeMillis();
        if (fileIO) {
            in = new FastReader("");
            out = new PrintWriter("");
        } else {
            in = new FastReader();
            out = new PrintWriter(System.out);
        }
        //Solution Credits: Taranpreet Singh
        int T = multipleTC? ni():1;
        pre();
        for (int t = 1; t <= T; t++) solve(t);
        out.flush();
        out.close();
        System.err.println(System.currentTimeMillis() - ct);
    }
    public static void main(String[] args) throws Exception{
        if(memory)new Thread(null, new Runnable() {public void run(){try{new Main().run();}catch(Exception e){e.printStackTrace();}}}, "1", 1 << 28).start();
        else new Main().run();
    }
    int[][] make(int n, int e, int[] from, int[] to, boolean f){
        int[][] g = new int[n][];int[]cnt = new int[n];
        for(int i = 0; i< e; i++){
            cnt[from[i]]++;
            if(f)cnt[to[i]]++;
        }
        for(int i = 0; i< n; i++)g[i] = new int[cnt[i]];
        for(int i = 0; i< e; i++){
            g[from[i]][--cnt[from[i]]] = to[i];
            if(f)g[to[i]][--cnt[to[i]]] = from[i];
        }
        return g;
    }
    int[][][] makeS(int n, int e, int[] from, int[] to, boolean f){
        int[][][] g = new int[n][][];int[]cnt = new int[n];
        for(int i = 0; i< e; i++){
            cnt[from[i]]++;
            if(f)cnt[to[i]]++;
        }
        for(int i = 0; i< n; i++)g[i] = new int[cnt[i]][];
        for(int i = 0; i< e; i++){
            g[from[i]][--cnt[from[i]]] = new int[]{to[i], i, 0};
            if(f)g[to[i]][--cnt[to[i]]] = new int[]{from[i], i, 1};
        }
        return g;
    }
    int find(int[] set, int u){return set[u] = (set[u] == u?u:find(set, set[u]));}
    int digit(long s){int ans = 0;while(s>0){s/=10;ans++;}return ans;}
    long gcd(long a, long b){return (b==0)?a:gcd(b,a%b);}
    int gcd(int a, int b){return (b==0)?a:gcd(b,a%b);}
    int bit(long n){return (n==0)?0:(1+bit(n&(n-1)));}
    void p(Object... o){for(Object oo:o)out.print(oo+" ");}
    void pn(Object... o){for(Object oo:o)out.print(oo+" ");out.println();}
    void pni(Object... o){for(Object oo:o)out.println(oo+" ");out.println();out.flush();}
    String n()throws Exception{return in.next();}
    String nln()throws Exception{return in.nextLine();}
    int ni()throws Exception{return Integer.parseInt(in.next());}
    long nl()throws Exception{return Long.parseLong(in.next());}
    double nd()throws Exception{return Double.parseDouble(in.next());}

    class FastReader{
        BufferedReader br;
        StringTokenizer st;
        public FastReader(){
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        public FastReader(String s) throws Exception{
            br = new BufferedReader(new FileReader(s));
        }

        String next() throws Exception{
            while (st == null || !st.hasMoreElements()){
                try{
                    st = new StringTokenizer(br.readLine());
                }catch (IOException  e){
                    throw new Exception(e.toString());
                }
            }
            return st.nextToken();
        }

        String nextLine() throws Exception{
            String str;
            try{
                str = br.readLine();
            }catch (IOException e){
                throw new Exception(e.toString());
            }
            return str;
        }
    }
}