Problem: User ainta decided to make a new instant messenger called "aintalk". With aintalk, each user can chat with other people. User ainta made the prototype of some functions to implement this thing.

  1. login(u): User u logins into aintalk and becomes online. 
  2. logout(u): User u logouts and becomes offline. 
  3. add_friend(u, v): User u and user v become friends. It means, u and v can talk with each other. The friendship is bidirectional. 
  4. del_friend(u, v): Unfriend user u and user v. It means, u and v cannot talk with each other from then. 
  5. count_online_friends(u): The function returns the number of friends of user u who are online at the moment. 



Because the messenger is being tested by some users numbered from 1 to n, there is no register method. This means, at the beginning, some users may be online, and some users may have friends.

User ainta is going to make these functions, but before making the messenger public, he wants to know whether he is correct. Help ainta verify his code.

Input

The first line contains three space-separated integers n, m and q (1 ≤ n ≤ 50000; 1 ≤ m ≤ 150000; 1 ≤ q ≤ 250000) — the number of users, the number of pairs of friends, and the number of queries.

The second line contains an integer o (1 ≤ o ≤ n) — the number of online users at the beginning. The third line contains o space-separated integers x1, x2, ..., xo (1 ≤ xi ≤ n) — the ids of the online users. It is guaranteed that these values are distinct.

Each of the next m lines contains two space-separated integers ai and bi (1 ≤ ai, bi ≤ n; ai ≠ bi) — the ids of two users who are friends at the beginning. It is guaranteed there are no multiple friendship given in the input. Note that the friendship is bidirectional.

Next q lines describe the q queries in the format:

  * "O u" (1 ≤ u ≤ n) : Call online(u). It is guaranteed that user u was offline just before the function call. 
  * "F u" (1 ≤ u ≤ n) : Call offline(u). It is guaranteed that user u was online just before the function call. 
  * "A u v" (1 ≤ u, v ≤ n; u ≠ v) : Call add_friend(u, v). It is guaranteed that these two users weren't friends just before the function call. 
  * "D u v" (1 ≤ u, v ≤ n; u ≠ v) : Call del_friend(u, v). It is guaranteed that these two users were friends just before the function call. 
  * "C u" (1 ≤ u ≤ n) : Call count_online_friends(u) and print the result in a single line. 

Output

For each count_online_friends(u) query, print the required answer in a single line. 

Examples

Input

5 2 9
1
4
1 3
3 4
C 3
A 2 5
O 1
D 1 3
A 1 2
A 4 2
C 2
F 4
C 2


Output

1
2
1

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.PrintWriter;
import java.util.InputMismatchException;
import java.util.HashSet;
import java.io.InputStream;

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

class TaskD {
    boolean[] isOnline;
    HashSet<Integer>[] S;
    HashSet<Integer>[] H;
    int[] O;
    int C;

    public void solve(int testNumber, InputReader in, PrintWriter out) {
        int N = in.nextInt();
        int M = in.nextInt();
        int Q = in.nextInt();
        isOnline = new boolean[N];
        int numOnline = in.nextInt();
        for (int i = 0; i < numOnline; i++) {
            int a = in.nextInt() - 1;
            isOnline[a] = true;
        }

        S = new HashSet[N];
        for (int i = 0; i < N; i++) {
            S[i] = new HashSet<Integer>();
        }
        H = new HashSet[N];
        for (int i = 0; i < N; i++) {
            H[i] = new HashSet<Integer>();
        }
        O = new int[N];
//        C = 0;
//        while ((C + 1) * (C + 1) <= M) {
//            C++;
//        }
        C = 450;

        for (int i = 0; i < M; i++) {
            int a = in.nextInt() - 1;
            int b = in.nextInt() - 1;
            addFriendship(a, b);
        }

        while (Q-- > 0) {
            char t = in.nextCharacter();
            int a = in.nextInt() - 1;

            if (t == 'O') {
                goOnline(a);
            }
            else if (t == 'F') {
                goOffline(a);
            }
            else if (t == 'A') {
                int b = in.nextInt() - 1;
                addFriendship(a, b);
            }
            else if (t == 'D') {
                int b = in.nextInt() - 1;
                deleteFriendship(a, b);
            }
            else if (t == 'C') {
                int ans = countOnlineFriends(a);
                out.println(ans);
            }
        }
    }

    private int countOnlineFriends(int a) {
        int ret = O[a];
        for (int x : H[a]) {
            if (isOnline[x]) {
                ret++;
            }
        }
        return ret;
    }

    private void deleteFriendship(int a, int b) {
        singleDeleteFriendship(a, b);
        singleDeleteFriendship(b, a);
        S[a].remove(b);
        S[b].remove(a);
        removeFriendshipEdge(a, b);
        removeFriendshipEdge(b, a);
    }

    private void removeFriendshipEdge(int a, int b) {
        if (S[b].size() >= C) {
            H[a].remove(b);
        }
        else {
            if (isOnline[b]) {
                O[a]--;
            }
        }
    }

    /*
        b is no longer the friend of a
     */
    private void singleDeleteFriendship(int a, int b) {
        int numFriends = S[a].size();

        if (numFriends == C) { // becomes light
            for (int x : S[a]) {
                H[x].remove(a);
                if (isOnline[a]) {
                    O[x]++;
                }
            }
        }
    }

    private void addFriendship(int a, int b) {
        int aFriends = S[a].size();
        int bFriends = S[b].size();
        singleAddFriendship(a, b, aFriends);
        S[a].add(b);
        S[b].add(a);
        singleAddFriendship(b, a, bFriends);
    }

    /*
        b becomes the friend of a
    */
    private void singleAddFriendship(int a, int b, int numFriends) {
        if (numFriends + 1 == C) { // becomes heavy
            for (int x : S[a]) {
                if (isOnline[a]) {
                    O[x]--;
                }
                H[x].add(a);
            }
        }

        if (S[b].size() >= C) {
            H[a].add(b);
        }
        else {
            if (isOnline[b]) {
                O[a]++;
            }
        }
    }

    private void goOffline(int a) {
        int numFriends = S[a].size();
        if (numFriends < C) {
            for (int x : S[a]) {
                O[x]--;
            }
        }
        isOnline[a] = false;
    }

    private void goOnline(int a) {
        int numFriends = S[a].size();
        if (numFriends < C) {
            for (int x : S[a]) {
                O[x]++;
            }
        }
        isOnline[a] = true;
    }
}

class InputReader {
    private InputStream stream;
    private byte[] buf = new byte[1024];
    private int curChar;
    private int numChars;

    public InputReader(InputStream stream) {
        this.stream = stream;
    }

    public int read() {
        if (numChars == -1)
            throw new InputMismatchException();
        if (curChar >= numChars) {
            curChar = 0;
            try {
                numChars = stream.read(buf);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
            if (numChars <= 0)
                return -1;
        }
        return buf[curChar++];
    }

    public int nextInt() {
        return Integer.parseInt(nextString());
    }

    public String nextString() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        StringBuffer res = new StringBuffer();
        do {
            res.appendCodePoint(c);
            c = read();
        } while (!isSpaceChar(c));

        return res.toString();
    }

    public char nextCharacter() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        return (char) c;
    }

    private boolean isSpaceChar(int c) {
        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }

}