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.io.FileInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.nio.charset.Charset;
import java.util.*;


public class Ada {
    public static void main(String[] args) throws Exception {
        boolean local = System.getProperty("ONLINE_JUDGE") == null;
        boolean async = false;

        Charset charset = Charset.forName("ascii");

        FastIO io = local ? new FastIO(new FileInputStream("D:\\DATABASE\\TESTCASE\\Code.in"), System.out, charset) : new FastIO(System.in, System.out, charset);
        Task task = new Task(io, new Debug(local));

        if (async) {
            Thread t = new Thread(null, task, "dalt", 1 << 27);
            t.setPriority(Thread.MAX_PRIORITY);
            t.start();
            t.join();
        } else {
            task.run();
        }

        if (local) {
            io.cache.append("\n\n--memory -- \n" + ((Runtime.getRuntime().totalMemory() - Runtime.getRuntime().freeMemory()) >> 20) + "M");
        }

        io.flush();
    }

    public static class Task implements Runnable {
        final FastIO io;
        final Debug debug;
        long inf = (long) 1e10;

        public Task(FastIO io, Debug debug) {
            this.io = io;
            this.debug = debug;
        }

        @Override
        public void run() {
            solve();
        }


        public void solve() {
            char[] data = new char[200000];
            int len = io.readString(data, 0);

            char[] words = new char[200000];

            ACAutomaton l2r = new ACAutomaton();
            ACAutomaton r2l = new ACAutomaton();

            int n = io.readInt();

            for (int i = 0; i < n; i++) {
                int cnt = io.readString(words, 0);
                l2r.beginBuilding();
                r2l.beginBuilding();
                for (int j = 0, k = cnt - 1; j < cnt; j++, k--) {
                    l2r.build(words[j]);
                    r2l.build(words[k]);
                }
                l2r.buildLast.cnt++;
                r2l.buildLast.cnt++;
            }

            l2r.endBuilding();
            r2l.endBuilding();

            r2l.beginMatching();
            int[] r2lData = new int[len];
            for (int i = len - 1; i >= 0; i--) {
                r2l.match(data[i]);
                r2lData[i] = r2l.matchLast.cnt;
            }

            long total = 0;
            l2r.beginMatching();
            for (int i = 0; i < len - 1; i++) {
                l2r.match(data[i]);
                total += (long)l2r.matchLast.cnt * r2lData[i + 1];
            }

            io.cache.append(total);
        }
    }


    /**
     * Created by dalt on 2018/5/25.
     */
    public static class ACAutomaton {
        static final int MIN_CHARACTER = 'a';
        static final int MAX_CHARACTER = 'z';
        static final int RANGE_SIZE = MAX_CHARACTER - MIN_CHARACTER + 1;
        Node root;
        Node buildLast;
        Node matchLast;
        List<Node> allNodes = new ArrayList(1);


        private Node addNode() {
            Node node = new Node();
            node.id = allNodes.size();
            allNodes.add(node);
            return node;
        }


        public ACAutomaton() {
            root = addNode();
        }

        public void beginBuilding() {
            buildLast = root;
        }

        public void endBuilding() {
            Deque<Node> deque = new ArrayDeque(allNodes.size());
            for (int i = 0; i < RANGE_SIZE; i++) {
                if (root.next[i] != null) {
                    deque.addLast(root.next[i]);
                }
            }

            while (!deque.isEmpty()) {
                Node head = deque.removeFirst();
                Node fail = visit(head.father.fail, head.index);
                if (fail == null) {
                    head.fail = root;
                } else {
                    head.fail = fail.next[head.index];
                }
                head.cnt = head.cnt + head.fail.cnt;
                for (int i = 0; i < RANGE_SIZE; i++) {
                    if (head.next[i] != null) {
                        deque.addLast(head.next[i]);
                    }
                }
            }

            for (int i = 0; i < RANGE_SIZE; i++) {
                if (root.next[i] != null) {
                    deque.addLast(root.next[i]);
                } else {
                    root.next[i] = root;
                }
            }
            while (!deque.isEmpty()) {
                Node head = deque.removeFirst();
                for (int i = 0; i < RANGE_SIZE; i++) {
                    if (head.next[i] != null) {
                        deque.addLast(head.next[i]);
                    } else {
                        head.next[i] = head.fail.next[i];
                    }
                }
            }
        }

        public Node visit(Node trace, int index) {
            while (trace != null && trace.next[index] == null) {
                trace = trace.fail;
            }
            return trace;
        }

        public void build(char c) {
            int index = c - MIN_CHARACTER;
            if (buildLast.next[index] == null) {
                Node node = addNode();
                node.father = buildLast;
                node.index = index;
                buildLast.next[index] = node;
            }
            buildLast = buildLast.next[index];
        }

        public void beginMatching() {
            matchLast = root;
        }

        public void match(char c) {
            int index = c - MIN_CHARACTER;
            matchLast = matchLast.next[index];
        }

        public static class Node {
            Node[] next = new Node[RANGE_SIZE];
            Node fail;
            Node father;
            int index;
            int id;
            int cnt;

            @Override
            public String toString() {
                return father == null ? "" : (father.toString() + (char) (MIN_CHARACTER + index));
            }
        }
    }

    public static class Randomized {
        static Random random = new Random();

        public static double nextDouble(double min, double max) {
            return random.nextDouble() * (max - min) + min;
        }

        public static void randomizedArray(int[] data, int from, int to) {
            to--;
            for (int i = from; i <= to; i++) {
                int s = nextInt(i, to);
                int tmp = data[i];
                data[i] = data[s];
                data[s] = tmp;
            }
        }

        public static void randomizedArray(long[] data, int from, int to) {
            to--;
            for (int i = from; i <= to; i++) {
                int s = nextInt(i, to);
                long tmp = data[i];
                data[i] = data[s];
                data[s] = tmp;
            }
        }

        public static void randomizedArray(double[] data, int from, int to) {
            to--;
            for (int i = from; i <= to; i++) {
                int s = nextInt(i, to);
                double tmp = data[i];
                data[i] = data[s];
                data[s] = tmp;
            }
        }

        public static void randomizedArray(float[] data, int from, int to) {
            to--;
            for (int i = from; i <= to; i++) {
                int s = nextInt(i, to);
                float tmp = data[i];
                data[i] = data[s];
                data[s] = tmp;
            }
        }

        public static <T> void randomizedArray(T[] data, int from, int to) {
            to--;
            for (int i = from; i <= to; i++) {
                int s = nextInt(i, to);
                T tmp = data[i];
                data[i] = data[s];
                data[s] = tmp;
            }
        }

        public static int nextInt(int l, int r) {
            return random.nextInt(r - l + 1) + l;
        }
    }

    /**
     * Mod operations
     */
    public static class Modular {
        int m;

        public Modular(int m) {
            this.m = m;
        }

        public int valueOf(int x) {
            x %= m;
            if (x < 0) {
                x += m;
            }
            return x;
        }

        public int valueOf(long x) {
            x %= m;
            if (x < 0) {
                x += m;
            }
            return (int) x;
        }

        public int mul(int x, int y) {
            return valueOf((long) x * y);
        }

        public int mul(long x, long y) {
            x = valueOf(x);
            y = valueOf(y);
            return valueOf(x * y);
        }

        public int plus(int x, int y) {
            return valueOf(x + y);
        }

        public int plus(long x, long y) {
            x = valueOf(x);
            y = valueOf(y);
            return valueOf(x + y);
        }

        @Override
        public String toString() {
            return "mod " + m;
        }
    }

    public static class FastIO {
        public final StringBuilder cache = new StringBuilder(1 << 20);
        private final InputStream is;
        private final OutputStream os;
        private final Charset charset;
        private StringBuilder defaultStringBuf = new StringBuilder(1 << 8);
        private byte[] buf = new byte[1 << 13];
        private int bufLen;
        private int bufOffset;
        private int next;

        public FastIO(InputStream is, OutputStream os, Charset charset) {
            this.is = is;
            this.os = os;
            this.charset = charset;
        }

        public FastIO(InputStream is, OutputStream os) {
            this(is, os, Charset.forName("ascii"));
        }

        private int read() {
            while (bufLen == bufOffset) {
                bufOffset = 0;
                try {
                    bufLen = is.read(buf);
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
                if (bufLen == -1) {
                    return -1;
                }
            }
            return buf[bufOffset++];
        }

        public void skipBlank() {
            while (next >= 0 && next <= 32) {
                next = read();
            }
        }

        public int readInt() {
            int sign = 1;

            skipBlank();
            if (next == '+' || next == '-') {
                sign = next == '+' ? 1 : -1;
                next = read();
            }

            int val = 0;
            if (sign == 1) {
                while (next >= '0' && next <= '9') {
                    val = val * 10 + next - '0';
                    next = read();
                }
            } else {
                while (next >= '0' && next <= '9') {
                    val = val * 10 - next + '0';
                    next = read();
                }
            }

            return val;
        }

        public long readLong() {
            int sign = 1;

            skipBlank();
            if (next == '+' || next == '-') {
                sign = next == '+' ? 1 : -1;
                next = read();
            }

            long val = 0;
            if (sign == 1) {
                while (next >= '0' && next <= '9') {
                    val = val * 10 + next - '0';
                    next = read();
                }
            } else {
                while (next >= '0' && next <= '9') {
                    val = val * 10 - next + '0';
                    next = read();
                }
            }

            return val;
        }

        public double readDouble() {
            boolean sign = true;
            skipBlank();
            if (next == '+' || next == '-') {
                sign = next == '+';
                next = read();
            }

            long val = 0;
            while (next >= '0' && next <= '9') {
                val = val * 10 + next - '0';
                next = read();
            }
            if (next != '.') {
                return sign ? val : -val;
            }
            next = read();
            long radix = 1;
            long point = 0;
            while (next >= '0' && next <= '9') {
                point = point * 10 + next - '0';
                radix = radix * 10;
                next = read();
            }
            double result = val + (double) point / radix;
            return sign ? result : -result;
        }

        public String readString(StringBuilder builder) {
            skipBlank();

            while (next > 32) {
                builder.append((char) next);
                next = read();
            }

            return builder.toString();
        }

        public String readString() {
            defaultStringBuf.setLength(0);
            return readString(defaultStringBuf);
        }

        public int readLine(char[] data, int offset) {
            int originalOffset = offset;
            while (next != -1 && next != '\n') {
                data[offset++] = (char) next;
                next = read();
            }
            return offset - originalOffset;
        }

        public int readString(char[] data, int offset) {
            skipBlank();

            int originalOffset = offset;
            while (next > 32) {
                data[offset++] = (char) next;
                next = read();
            }

            return offset - originalOffset;
        }

        public int readString(byte[] data, int offset) {
            skipBlank();

            int originalOffset = offset;
            while (next > 32) {
                data[offset++] = (byte) next;
                next = read();
            }

            return offset - originalOffset;
        }

        public char readChar() {
            skipBlank();
            char c = (char) next;
            next = read();
            return c;
        }

        public void flush() {
            try {
                os.write(cache.toString().getBytes(charset));
                os.flush();
                cache.setLength(0);
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }

        public boolean hasMore() {
            skipBlank();
            return next != -1;
        }
    }

    public static class Debug {
        private boolean allowDebug;

        public Debug(boolean allowDebug) {
            this.allowDebug = allowDebug;
        }

        public void assertTrue(boolean flag) {
            if (!allowDebug) {
                return;
            }
            if (!flag) {
                fail();
            }
        }

        public void fail() {
            throw new RuntimeException();
        }

        public void assertFalse(boolean flag) {
            if (!allowDebug) {
                return;
            }
            if (flag) {
                fail();
            }
        }

        private void outputName(String name) {
            System.out.print(name + " = ");
        }

        public void debug(String name, int x) {
            if (!allowDebug) {
                return;
            }

            outputName(name);
            System.out.println("" + x);
        }

        public void debug(String name, long x) {
            if (!allowDebug) {
                return;
            }
            outputName(name);
            System.out.println("" + x);
        }

        public void debug(String name, double x) {
            if (!allowDebug) {
                return;
            }
            outputName(name);
            System.out.println("" + x);
        }

        public void debug(String name, int[] x) {
            if (!allowDebug) {
                return;
            }
            outputName(name);
            System.out.println(Arrays.toString(x));
        }

        public void debug(String name, long[] x) {
            if (!allowDebug) {
                return;
            }
            outputName(name);
            System.out.println(Arrays.toString(x));
        }

        public void debug(String name, double[] x) {
            if (!allowDebug) {
                return;
            }
            outputName(name);
            System.out.println(Arrays.toString(x));
        }

        public void debug(String name, Object x) {
            if (!allowDebug) {
                return;
            }
            outputName(name);
            System.out.println("" + x);
        }

        public void debug(String name, Object... x) {
            if (!allowDebug) {
                return;
            }
            outputName(name);
            System.out.println(Arrays.deepToString(x));
        }
    }
}