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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
void getre() {
  int x = 0;
  printf("%d\n", 1 / x);
}
void gettle() {
  int res = 1;
  while (1) res <<= 1;
  printf("%d\n", res);
}
template <typename T, typename S>
inline bool upmin(T &a, const S &b) {
  return a > b ? a = b, 1 : 0;
}
template <typename T, typename S>
inline bool upmax(T &a, const S &b) {
  return a < b ? a = b, 1 : 0;
}
template <typename N, typename PN>
inline N flo(N a, PN b) {
  return a >= 0 ? a / b : -((-a - 1) / b) - 1;
}
template <typename N, typename PN>
inline N cei(N a, PN b) {
  return a > 0 ? (a - 1) / b + 1 : -(-a / b);
}
template <typename N>
N gcd(N a, N b) {
  return b ? gcd(b, a % b) : a;
}
template <typename N>
inline int sgn(N a) {
  return a > 0 ? 1 : (a < 0 ? -1 : 0);
}
inline void gn(long long &x) {
  int sg = 1;
  char c;
  while (((c = getchar()) < '0' || c > '9') && c != '-')
    ;
  c == '-' ? (sg = -1, x = 0) : (x = c - '0');
  while ((c = getchar()) >= '0' && c <= '9') x = x * 10 + c - '0';
  x *= sg;
}
inline void gn(int &x) {
  long long t;
  gn(t);
  x = t;
}
inline void gn(unsigned long long &x) {
  long long t;
  gn(t);
  x = t;
}
inline void gn(double &x) {
  double t;
  scanf("%lf", &t);
  x = t;
}
inline void gn(long double &x) {
  double t;
  scanf("%lf", &t);
  x = t;
}
inline void gs(char *s) { scanf("%s", s); }
inline void gc(char &c) {
  while ((c = getchar()) > 126 || c < 33)
    ;
}
inline void pc(char c) { putchar(c); }
inline long long sqr(long long a) { return a * a; }
inline double sqrf(double a) { return a * a; }
const int inf = 0x3f3f3f3f;
const double pi = 3.14159265358979323846264338327950288L;
const double eps = 1e-6;
const int hashtable_mod = 5000011;
const int hashtable_maxn = 1111111;
struct hashtable {
  int head[hashtable_mod];
  long long s[hashtable_maxn];
  int v[hashtable_maxn], zerovalue;
  int next[hashtable_maxn];
  int label[hashtable_mod];
  int tot;
  int tms;
  int &operator[](long long S) {
    int la = abs(S) % hashtable_mod;
    if (label[la] == tms)
      for (int st = head[la]; st; st = next[st])
        if (s[st] == S) return v[st];
    ++tot;
    v[tot] = zerovalue;
    s[tot] = S;
    next[tot] = label[la] == tms ? head[la] : 0;
    head[la] = tot;
    label[la] = tms;
    return v[tot];
  }
  void clear() {
    tms++;
    tot = 0;
  }
} has;
int n, m, q;
const int big = 400;
int col[55555];
int smalans[55555];
int deg[55555];
vector<pair<int, int> > g[55555];
int biglist[55555], btot = 0;
int isbig[55555];
int query(int x) {
  int ret = 0;
  for (int i = (1), _ed = (btot + 1); i < _ed; i++) {
    int v = biglist[i];
    if (col[biglist[i]] && has[(1ll * min(x, v)) << 32 | max(x, v)]) ret++;
  }
  return ret + smalans[x];
}
namespace fastIO_hqz {
bool IOerror = 0;
inline char nc() {
  static char buf[100000], *p1 = buf + 100000, *pend = buf + 100000;
  if (p1 == pend) {
    p1 = buf;
    pend = buf + fread(buf, 1, 100000, stdin);
    if (pend == p1) {
      IOerror = 1;
      return -1;
    }
  }
  return *p1++;
}
inline bool blank(char ch) {
  return ch == ' ' || ch == '\n' || ch == '\r' || ch == '\t';
}
inline void read(int &x) {
  bool sign = 0;
  char ch = nc();
  x = 0;
  for (; blank(ch); ch = nc())
    ;
  if (IOerror) return;
  if (ch == '-') sign = 1, ch = nc();
  for (; ch >= '0' && ch <= '9'; ch = nc()) x = x * 10 + ch - '0';
  if (sign) x = -x;
}
inline void read(long long &x) {
  bool sign = 0;
  char ch = nc();
  x = 0;
  for (; blank(ch); ch = nc())
    ;
  if (IOerror) return;
  if (ch == '-') sign = 1, ch = nc();
  for (; ch >= '0' && ch <= '9'; ch = nc()) x = x * 10 + ch - '0';
  if (sign) x = -x;
}
inline void read(double &x) {
  bool sign = 0;
  char ch = nc();
  x = 0;
  for (; blank(ch); ch = nc())
    ;
  if (IOerror) return;
  if (ch == '-') sign = 1, ch = nc();
  for (; ch >= '0' && ch <= '9'; ch = nc()) x = x * 10 + ch - '0';
  if (ch == '.') {
    double tmp = 1;
    ch = nc();
    for (; ch >= '0' && ch <= '9'; ch = nc())
      tmp /= 10.0, x += tmp * (ch - '0');
  }
  if (sign) x = -x;
}
inline void read(char *s) {
  char ch = nc();
  for (; blank(ch); ch = nc())
    ;
  if (IOerror) return;
  for (; !blank(ch) && !IOerror; ch = nc()) *s++ = ch;
  *s = 0;
}
inline void read(char &c) {
  for (c = nc(); blank(c); c = nc())
    ;
  if (IOerror) {
    c = -1;
    return;
  }
}
inline void read1(int &x) {
  char ch;
  int bo = 0;
  x = 0;
  for (ch = getchar(); ch < '0' || ch > '9'; ch = getchar())
    if (ch == '-') bo = 1;
  for (; ch >= '0' && ch <= '9'; x = x * 10 + ch - '0', ch = getchar())
    ;
  if (bo) x = -x;
}
inline void read1(long long &x) {
  char ch;
  int bo = 0;
  x = 0;
  for (ch = getchar(); ch < '0' || ch > '9'; ch = getchar())
    if (ch == '-') bo = 1;
  for (; ch >= '0' && ch <= '9'; x = x * 10 + ch - '0', ch = getchar())
    ;
  if (bo) x = -x;
}
inline void read1(double &x) {
  char ch;
  int bo = 0;
  x = 0;
  for (ch = getchar(); ch < '0' || ch > '9'; ch = getchar())
    if (ch == '-') bo = 1;
  for (; ch >= '0' && ch <= '9'; x = x * 10 + ch - '0', ch = getchar())
    ;
  if (ch == '.') {
    double tmp = 1;
    for (ch = getchar(); ch >= '0' && ch <= '9';
         tmp /= 10.0, x += tmp * (ch - '0'), ch = getchar())
      ;
  }
  if (bo) x = -x;
}
inline void read1(char *s) {
  char ch = getchar();
  for (; blank(ch); ch = getchar())
    ;
  for (; !blank(ch); ch = getchar()) *s++ = ch;
  *s = 0;
}
inline void read1(char &c) {
  for (c = getchar(); blank(c); c = getchar())
    ;
}
inline void read2(int &x) { scanf("%d", &x); }
inline void read2(long long &x) { scanf("%lld", &x); }
inline void read2(double &x) { scanf("%lf", &x); }
inline void read2(char *s) { scanf("%s", s); }
inline void read2(char &c) { scanf(" %c", &c); }
inline void readln2(char *s) { gets(s); }
struct Ostream_fwrite {
  char *buf, *p1, *pend;
  Ostream_fwrite() {
    buf = new char[100000];
    p1 = buf;
    pend = buf + 100000;
  }
  void out(char ch) {
    if (p1 == pend) {
      fwrite(buf, 1, 100000, stdout);
      p1 = buf;
    }
    *p1++ = ch;
  }
  void print(int x) {
    static char s[15], *s1;
    s1 = s;
    if (!x) *s1++ = '0';
    if (x < 0) out('-'), x = -x;
    while (x) *s1++ = x % 10 + '0', x /= 10;
    while (s1-- != s) out(*s1);
  }
  void println(int x) {
    static char s[15], *s1;
    s1 = s;
    if (!x) *s1++ = '0';
    if (x < 0) out('-'), x = -x;
    while (x) *s1++ = x % 10 + '0', x /= 10;
    while (s1-- != s) out(*s1);
    out('\n');
  }
  void print(long long x) {
    static char s[25], *s1;
    s1 = s;
    if (!x) *s1++ = '0';
    if (x < 0) out('-'), x = -x;
    while (x) *s1++ = x % 10 + '0', x /= 10;
    while (s1-- != s) out(*s1);
  }
  void println(long long x) {
    static char s[25], *s1;
    s1 = s;
    if (!x) *s1++ = '0';
    if (x < 0) out('-'), x = -x;
    while (x) *s1++ = x % 10 + '0', x /= 10;
    while (s1-- != s) out(*s1);
    out('\n');
  }
  void print(double x, int y) {
    static long long mul[] = {1,
                              10,
                              100,
                              1000,
                              10000,
                              100000,
                              1000000,
                              10000000,
                              100000000,
                              1000000000,
                              10000000000LL,
                              100000000000LL,
                              1000000000000LL,
                              10000000000000LL,
                              100000000000000LL,
                              1000000000000000LL,
                              10000000000000000LL,
                              100000000000000000LL};
    if (x < -1e-12) out('-'), x = -x;
    x *= mul[y];
    long long x1 = (long long)floor(x);
    if (x - floor(x) >= 0.5) ++x1;
    long long x2 = x1 / mul[y], x3 = x1 - x2 * mul[y];
    print(x2);
    if (y > 0) {
      out('.');
      for (size_t i = 1; i < y && x3 * mul[i] < mul[y]; out('0'), ++i)
        ;
      print(x3);
    }
  }
  void println(double x, int y) {
    print(x, y);
    out('\n');
  }
  void print(char *s) {
    while (*s) out(*s++);
  }
  void println(char *s) {
    while (*s) out(*s++);
    out('\n');
  }
  void flush() {
    if (p1 != buf) {
      fwrite(buf, 1, p1 - buf, stdout);
      p1 = buf;
    }
  }
  ~Ostream_fwrite() { flush(); }
} Ostream;
inline void print(int x) { Ostream.print(x); }
inline void println(int x) { Ostream.println(x); }
inline void print(char x) { Ostream.out(x); }
inline void println(char x) {
  Ostream.out(x);
  Ostream.out('\n');
}
inline void print(long long x) { Ostream.print(x); }
inline void println(long long x) { Ostream.println(x); }
inline void print(double x, int y) { Ostream.print(x, y); }
inline void println(double x, int y) { Ostream.println(x, y); }
inline void print(char *s) { Ostream.print(s); }
inline void println(char *s) { Ostream.println(s); }
inline void println() { Ostream.out('\n'); }
inline void flush() { Ostream.flush(); }
char Out[100000], *o = Out;
inline void print1(int x) {
  static char buf[15];
  char *p1 = buf;
  if (!x) *p1++ = '0';
  if (x < 0) *o++ = '-', x = -x;
  while (x) *p1++ = x % 10 + '0', x /= 10;
  while (p1-- != buf) *o++ = *p1;
}
inline void println1(int x) {
  print1(x);
  *o++ = '\n';
}
inline void print1(long long x) {
  static char buf[25];
  char *p1 = buf;
  if (!x) *p1++ = '0';
  if (x < 0) *o++ = '-', x = -x;
  while (x) *p1++ = x % 10 + '0', x /= 10;
  while (p1-- != buf) *o++ = *p1;
}
inline void println1(long long x) {
  print1(x);
  *o++ = '\n';
}
inline void print1(char c) { *o++ = c; }
inline void println1(char c) {
  *o++ = c;
  *o++ = '\n';
}
inline void print1(char *s) {
  while (*s) *o++ = *s++;
}
inline void println1(char *s) {
  print1(s);
  *o++ = '\n';
}
inline void println1() { *o++ = '\n'; }
inline void flush1() {
  if (o != Out) {
    if (*(o - 1) == '\n') *--o = 0;
    puts(Out);
  }
}
struct puts_write {
  ~puts_write() { flush1(); }
} _puts;
inline void print2(int x) { printf("%d", x); }
inline void println2(int x) { printf("%d\n", x); }
inline void print2(char x) { printf("%c", x); }
inline void println2(char x) { printf("%c\n", x); }
inline void print2(long long x) { printf("%lld", x); }
inline void println2(long long x) {
  print2(x);
  printf("\n");
}
inline void println2() { printf("\n"); }
};  // namespace fastIO_hqz
using namespace fastIO_hqz;
struct quer {
  char opt;
  int a, b;
} ques[555555];
int main() {
  read(n);
  read(m);
  read(q);
  int o;
  read(o);
  for (int i = (1), _ed = (o + 1); i < _ed; i++) {
    int x;
    read(x);
    col[x] = 1;
  }
  while (m--) {
    int x, y;
    read(x);
    read(y);
    if (x > y) swap(x, y);
    deg[x]++;
    deg[y]++;
    g[x].push_back(make_pair(y, 1));
    g[y].push_back(make_pair(x, 1));
    has[(1ll * x) << 32 | y] = 1;
  }
  for (int i = (1), _ed = (q + 1); i < _ed; i++) {
    char opt;
    read(opt);
    if (opt == 'C' || opt == 'O' || opt == 'F') {
      int u;
      read(u);
      ques[i] = (quer){opt, u, 0};
    } else {
      int a, b;
      read(a);
      read(b);
      if (a > b) swap(a, b);
      ques[i] = (quer){opt, a, b};
      deg[a]++;
      deg[b]++;
    }
  }
  for (int u = (1), _ed = (n + 1); u < _ed; u++) {
    if (deg[u] >= big) {
      biglist[++btot] = u;
      isbig[u] = 1;
    }
  }
  for (int u = (1), _ed = (n + 1); u < _ed; u++) {
    for (int i = (0), _ed = (((int)(g[u]).size())); i < _ed; i++) {
      if (col[g[u][i].first] && !isbig[g[u][i].first]) smalans[u]++;
    }
  }
  for (int i = (1), _ed = (q + 1); i < _ed; i++) {
    char opt = ques[i].opt;
    int u = ques[i].a, v = ques[i].b;
    if (opt == 'C') {
      printf("%d\n", query(u));
    } else if (opt == 'O') {
      col[u] = 1;
      if (!isbig[u]) {
        for (int i = (0), _ed = (((int)(g[u]).size())); i < _ed; i++)
          smalans[g[u][i].first] += g[u][i].second;
      }
    } else if (opt == 'F') {
      col[u] = 0;
      if (!isbig[u]) {
        for (int i = (0), _ed = (((int)(g[u]).size())); i < _ed; i++)
          smalans[g[u][i].first] -= g[u][i].second;
      }
    } else if (opt == 'A') {
      g[u].push_back(make_pair(v, 1));
      g[v].push_back(make_pair(u, 1));
      has[(1ll * u) << 32 | v] = 1;
      if (col[u] && !isbig[u]) smalans[v]++;
      if (col[v] && !isbig[v]) smalans[u]++;
    } else if (opt == 'D') {
      g[u].push_back(make_pair(v, -1));
      g[v].push_back(make_pair(u, -1));
      has[(1ll * u) << 32 | v] = 0;
      if (col[u] && !isbig[u]) smalans[v]--;
      if (col[v] && !isbig[v]) smalans[u]--;
    }
  }
  return 0;
}