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.*;
import java.util.*;
public class D398 {
	static HashSet<Integer>[] g;
	static boolean[] mark;
	static boolean[] online;
	static int[] deg;
	static int[] res;
	static int[] friendly;
	static boolean[] wasOnline;
	static int friendlyCount = 0;
public static void main(String[] args) throws IOException {
	input.init(System.in);
	PrintWriter out = new PrintWriter(System.out);
	Random r = new Random();
	int n = input.nextInt(), m = input.nextInt(), q = input.nextInt();
	if(n < 900)
	{
		int o = input.nextInt();
		boolean[] online = new boolean[n];
		for(int i = 0; i<o; i++) online[input.nextInt()-1] = true;
		boolean[][] adj = new boolean[n][n];
		for(int i = 0; i<m; i++)
		{
			int a = input.nextInt()-1, b = input.nextInt()-1;
			adj[a][b] = adj[b][a] = true;
		}
		for(int i = 0; i<q; i++)
		{
			char c = input.next().charAt(0);
			if(c == 'O' || c == 'F')
			{
				int u = input.nextInt()-1;
				online[u] ^= true;
			}
			else if(c == 'A' || c == 'D')
			{
				int a = input.nextInt()-1, b = input.nextInt()-1;
				adj[a][b] ^= true;
				adj[b][a] ^= true;
			}
			else
			{
				int u = input.nextInt()-1, res = 0;
				for(int e = 0; e<n; e++)
				{
					if(adj[u][e] && online[e])
					{
						res++;
					}
				}
				out.println(res);
			}
		}
		out.close();
		return;
	}
	friendly = new int[n];
	res = new int[n];
	deg = new int[n];
	wasOnline = new boolean[n];
	online = new boolean[n];
	mark = new boolean[n];
	g = new HashSet[n];
	for(int i = 0; i<n; i++) g[i] = new HashSet<Integer>();
	int o = input.nextInt();
	int s = 400 + r.nextInt(200);
	for(int i = 0; i<o; i++) online[input.nextInt()-1] = true;
	for(int i = 0; i<m; i++)
	{
		int a = input.nextInt()-1, b = input.nextInt()-1;
		g[a].add(b);
		g[b].add(a);
		if(!mark[a] && online[a]) res[b]++;
		if(!mark[b] && online[b]) res[a]++;
		if(mark[a] && wasOnline[a]) res[b]++;
		if(mark[b] && wasOnline[b]) res[a]++;
		deg[a]++;
		deg[b]++;
		if(!mark[a] && deg[a] == s) makeFriendly(a);
		if(!mark[b] && deg[b] == s) makeFriendly(b);
	}
	for(int qq = 0; qq<q; qq++)
	{
		char c = input.next().charAt(0);
		if(c == 'O')
		{
			int u = input.nextInt()-1;
			online[u] = true;
			if(!mark[u])
			{
				for(int e : g[u]) res[e]++;
			}
		}
		else if(c == 'F')
		{
			int u = input.nextInt()-1;
			online[u] = false;
			if(!mark[u])
			{
				for(int e : g[u]) res[e]--;
			}
		}
		else if(c == 'A')
		{
			int a = input.nextInt()-1, b = input.nextInt()-1;
			g[a].add(b);
			g[b].add(a);
			if(!mark[a] && online[a]) res[b]++;
			if(!mark[b] && online[b]) res[a]++;
			if(mark[a] && wasOnline[a]) res[b]++;
			if(mark[b] && wasOnline[b]) res[a]++;
			deg[a]++;
			deg[b]++;
			if(!mark[a] && deg[a] == s) makeFriendly(a);
			if(!mark[b] && deg[b] == s) makeFriendly(b);
		}
		else if(c == 'D')
		{
			int a = input.nextInt()-1, b = input.nextInt()-1;
			g[a].remove(b);
			g[b].remove(a);
			if(!mark[a] && online[a]) res[b]--;
			if(!mark[b] && online[b]) res[a]--;
			if(mark[a] && wasOnline[a]) res[b]--;
			if(mark[b] && wasOnline[b]) res[a]--;
			deg[a]--;
			deg[b]--;
		}
		else
		{
			out.println(count(input.nextInt()-1));
		}
	}
	out.close();
}
static void makeFriendly(int x)
{
	mark[x] = true;
	friendly[friendlyCount++] = x;
	wasOnline[x] = online[x];
	//if(online[x]) for(int e : g[x]) res[e]--;
}
static int count(int x)
{
	int r = res[x];
	for(int i = 0; i<friendlyCount; i++) 
	{
		int e = friendly[i];
		if(g[x].contains(e))
		{
			if(online[e]) r++;
			if(wasOnline[e]) r--;
			
		}
	}
	return r;
}
public static class input {
	static BufferedReader reader;
	static StringTokenizer tokenizer;

	static void init(InputStream input) {
		reader = new BufferedReader(new InputStreamReader(input));
		tokenizer = new StringTokenizer("");
	}

	static String next() throws IOException {
		while (!tokenizer.hasMoreTokens())
			tokenizer = new StringTokenizer(reader.readLine());
		return tokenizer.nextToken();
	}

	static int nextInt() throws IOException {
		return Integer.parseInt(next());
	}

	static double nextDouble() throws IOException {
		return Double.parseDouble(next());
	}

	static long nextLong() throws IOException {
		return Long.parseLong(next());
	}
}
}