Problem: Escape

An undirected graph with positive values ​​at the vertices is given. The vertices are numbered from 1 to N, and the i-th vertex has a value of w_i. You can start from the first vertex and move on the graph with the constraint that you cannot pass the edge that you just passed. At each vertex, you can get the score of the value that the vertex has only when you visit it for the first time.

Find the maximum sum of the points you can get.

Constraints

* 1 ≤ N ≤ 100000
* N − 1 ≤ M ≤ 100000
* 1 ≤ w_i ≤ 1000
* 1 ≤ u_i, v_i ≤ N
* There are no multiple edges or self edges
* The graph is concatenated



Input Format

Input is given from standard input in the following format.


N M
w_1 w_2 ... w_N
u_1 v_1
u_2 v_2
...
u_M v_M


In the first line, the number of vertices N of the graph and the integer M representing the number of edges are entered.
The value w_i of each vertex is entered in the second line.
In addition, the number of the two vertices connected by each side is entered in the M line.


Output Format

Print the answer on one line.

Sample Input 1


6 6
1 2 3 4 5 6
1 2
twenty three
3 4
14
4 5
5 6


Sample Output 1


twenty one


<image>
You can collect the points of all vertices by going from vertices 1 → 2 → 3 → 4 → 5 → 6.

Sample Input 2


7 8
1 3 3 5 2 2 3
1 2
twenty three
3 1
14
1 7
1 5
1 6
5 6


Sample Output 2


16


<image>
You can collect 16 points by going from vertices 1 → 2 → 3 → 1 → 5 → 6 → 1 → 4.





Example

Input

6 6
1 2 3 4 5 6
1 2
2 3
3 4
1 4
4 5
5 6


Output

21

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.io.UncheckedIOException;
import java.util.List;
import java.nio.charset.Charset;
import java.util.StringTokenizer;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.BufferedReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author mikit
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        LightScanner in = new LightScanner(inputStream);
        LightWriter out = new LightWriter(outputStream);
        ETourism solver = new ETourism();
        solver.solve(1, in, out);
        out.close();
    }

    static class ETourism {
        public void solve(int testNumber, LightScanner in, LightWriter out) {
            WithMoreStack.run(() -> {
                int n = in.ints(), m = in.ints();
                ETourism.City[] cities = new ETourism.City[n];
                for (int i = 0; i < n; i++) {
                    cities[i] = new ETourism.City(i, in.longs());
                }
                for (int i = 0; i < m; i++) {
                    int x = in.ints() - 1, y = in.ints() - 1;
                    cities[x].neighbor.add(cities[y]);
                    cities[y].neighbor.add(cities[x]);
                }
                int s = 0;
                cities[s].dfs(null);
                long base = 0;
                for (int i = 0; i < n; i++) {
                    cities[i].visited = false;
                    if (cities[i].cyclic) base += cities[i].value;
                }
                out.ans(base + cities[s].solve(null)).ln();
            });
        }

        private static class City {
            int index;
            long value;
            List<ETourism.City> neighbor = new ArrayList<>();
            boolean visited;
            boolean cyclic;

            City(int index, long value) {
                this.index = index;
                this.value = value;
            }

            boolean dfs(ETourism.City from) {
                visited = true;
                for (ETourism.City city : neighbor) {
                    if (city == from) continue;
                    if (city.visited || city.dfs(this)) cyclic = true;
                }
                return cyclic;
            }

            long solve(ETourism.City from) {
                long max = 0;
                visited = true;
                for (ETourism.City city : neighbor) {
                    if (city == from || city.visited) continue;
                    max = Math.max(max, city.solve(this));
                }
                if (!cyclic) max += value;
                return max;
            }

        }

    }

    static class LightWriter implements AutoCloseable {
        private final Writer out;
        private boolean autoflush = false;
        private boolean breaked = true;

        public LightWriter(Writer out) {
            this.out = out;
        }

        public LightWriter(OutputStream out) {
            this(new BufferedWriter(new OutputStreamWriter(out, Charset.defaultCharset())));
        }

        public LightWriter print(char c) {
            try {
                out.write(c);
                breaked = false;
            } catch (IOException ex) {
                throw new UncheckedIOException(ex);
            }
            return this;
        }

        public LightWriter print(String s) {
            try {
                out.write(s, 0, s.length());
                breaked = false;
            } catch (IOException ex) {
                throw new UncheckedIOException(ex);
            }
            return this;
        }

        public LightWriter ans(String s) {
            if (!breaked) {
                print(' ');
            }
            return print(s);
        }

        public LightWriter ans(long l) {
            return ans(Long.toString(l));
        }

        public LightWriter ln() {
            print(System.lineSeparator());
            breaked = true;
            if (autoflush) {
                try {
                    out.flush();
                } catch (IOException ex) {
                    throw new UncheckedIOException(ex);
                }
            }
            return this;
        }

        public void close() {
            try {
                out.close();
            } catch (IOException ex) {
                throw new UncheckedIOException(ex);
            }
        }

    }

    static class LightScanner {
        private BufferedReader reader = null;
        private StringTokenizer tokenizer = null;

        public LightScanner(InputStream in) {
            reader = new BufferedReader(new InputStreamReader(in));
        }

        public String string() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new UncheckedIOException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int ints() {
            return Integer.parseInt(string());
        }

        public long longs() {
            return Long.parseLong(string());
        }

    }

    static class WithMoreStack {
        private static final long STACK_SIZE = 64L * 1000 * 1000;

        private WithMoreStack() {
        }

        public static void run(Runnable task) {
            try {
                Thread thread = new Thread(null, task, "run", STACK_SIZE);
                thread.start();
                thread.join();
            } catch (InterruptedException ignored) {
            }
        }

    }
}