Problem p03354 (C++)

Buggy submission (status: Runtime Error):
// include
//------------------------------------------
#include <algorithm>
#include <bitset>
#include <cctype>
#include <climits>
#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <ctime>
#include <deque>
#include <functional>
#include <iomanip>
#include <iostream>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <utility>
#include <vector>

using namespace std;

// typedef
//------------------------------------------
typedef long long LL;
typedef vector<int> VI;
typedef vector<bool> VB;
typedef vector<char> VC;
typedef vector<double> VD;
typedef vector<string> VS;
typedef vector<LL> VLL;
typedef vector<VI> VVI;
typedef vector<VB> VVB;
typedef vector<VS> VVS;
typedef vector<VLL> VVLL;
typedef vector<VVI> VVVI;
typedef pair<int, int> PII;
typedef pair<LL, LL> PLL;
typedef pair<int, string> PIS;
typedef pair<string, int> PSI;
typedef pair<string, string> PSS;

// 数値・文字列
//------------------------------------------
inline int toInt(string s) {
  int v;
  istringstream sin(s);
  sin >> v;
  return v;
}

inline LL toLongLong(string s) {
  LL v;
  istringstream sin(s);
  sin >> v;
  return v;
}

template <class T> inline string toString(T x) {
  ostringstream sout;
  sout << x;
  return sout.str();
}

inline VC toVC(string s) {
  VC data(s.begin(), s.end());
  return data;
}

template <typename List>
void SPRIT(const std::string &s, const std::string &delim, List &result) {
  result.clear();
  string::size_type pos = 0;
  while (pos != string::npos) {
    string::size_type p = s.find(delim, pos);
    if (p == string::npos) {
      result.push_back(s.substr(pos));
      break;
    } else {
      result.push_back(s.substr(pos, p - pos));
    }
    pos = p + delim.size();
  }
}

string TRIM(const string &str, const char *trimCharacterList = " \t\v\r\n") {
  string result;
  string::size_type left = str.find_first_not_of(trimCharacterList);
  if (left != string::npos) {
    string::size_type right = str.find_last_not_of(trimCharacterList);
    result = str.substr(left, right - left + 1);
  }
  return result;
}

template <typename T> bool VECTOR_EXISTS(vector<T> vec, T data) {
  auto itr = std::find(vec.begin(), vec.end(), data);
  size_t index = distance(vec.begin(), itr);
  if (index != vec.size()) {
    return true;
  } else {
    return 0;
  }
}

#define UPPER(s) transform((s).begin(), (s).end(), (s).begin(), ::toupper)
#define LOWER(s) transform((s).begin(), (s).end(), (s).begin(), ::tolower)

// 四捨五入 nLen=小数点第N位にする
//------------------------------------------

// 四捨五入
double ceil_n(double dIn, int nLen) {
  double dOut;
  dOut = dIn * pow(10.0, nLen);
  dOut = (double)(int)(dOut + 0.9);
  return dOut * pow(10.0, -nLen);
}

// 切り捨て
double floor_n(double dIn, int nLen) {
  double dOut;
  dOut = dIn * pow(10.0, nLen);
  dOut = (double)(int)(dOut);
  return dOut * pow(10.0, -nLen);
}

// 切り上げ
double round_n(double dIn, int nLen) {
  double dOut;
  dOut = dIn * pow(10.0, nLen);
  dOut = (double)(int)(dOut + 0.5);
  return dOut * pow(10.0, -nLen);
}

// n桁目の数の取得
int take_a_n(int num, int n) {
  string str = toString(num);
  return str[str.length() - n] - '0';
}

// 進数
//------------------------------------------

//"1111011" → 123
int strbase_2to10(const std::string &s) {
  int out = 0;
  for (int i = 0, size = s.size(); i < size; ++i) {
    out *= 2;
    out += ((int)s[i] == 49) ? 1 : 0;
  }
  return out;
}

//"123" → 1111011
int strbase_10to2(const std::string &s) {
  int binary = toInt(s);
  int out = 0;
  for (int i = 0; binary > 0; i++) {
    out = out + (binary % 2) * pow(static_cast<int>(10), i);
    binary = binary / 2;
  }
  return out;
}

//"ABC" 2748
int strbase_16to10(const std::string &s) {
  int out = stoi(s, 0, 16);
  return out;
}

// 1111011 → 123
int intbase_2to10(int in) {
  string str = toString(in);
  return strbase_2to10(str);
}

// 123 → 1111011
int intbase_10to2(int in) {
  string str = toString(in);
  return strbase_10to2(str);
}

int intbase_16to10(int in) {
  string str = toString(in);
  return strbase_16to10(str);
}

// 123→ "7B"
string intbase_10to16(unsigned int val, bool lower = true) {
  if (!val)
    return std::string("0");
  std::string str;
  const char hc = lower ? 'a' : 'A'; // 小文字 or 大文字表記
  while (val != 0) {
    int d = val & 15; // 16進数一桁を取得
    if (d < 10)
      str.insert(str.begin(), d + '0'); //  10未満の場合
    else                                //  10以上の場合
      str.insert(str.begin(), d - 10 + hc);
    val >>= 4;
  }
  return str;
}

// 整数を2進数表記したときの1の個数を返す
LL bitcount64(LL bits) {
  bits = (bits & 0x5555555555555555) + (bits >> 1 & 0x5555555555555555);
  bits = (bits & 0x3333333333333333) + (bits >> 2 & 0x3333333333333333);
  bits = (bits & 0x0f0f0f0f0f0f0f0f) + (bits >> 4 & 0x0f0f0f0f0f0f0f0f);
  bits = (bits & 0x00ff00ff00ff00ff) + (bits >> 8 & 0x00ff00ff00ff00ff);
  bits = (bits & 0x0000ffff0000ffff) + (bits >> 16 & 0x0000ffff0000ffff);
  return (bits & 0x00000000ffffffff) + (bits >> 32 & 0x00000000ffffffff);
}

// comparison
//------------------------------------------
#define C_MAX(a, b) ((a) > (b) ? (a) : (b))
#define C_MIN(a, b) ((a) < (b) ? (a) : (b))
#define C_ABS(a, b) ((a) < (b) ? (b) - (a) : (a) - (b))

// container util
//------------------------------------------
#define ALL(a) (a).begin(), (a).end()
#define RALL(a) (a).rbegin(), (a).rend()
#define SZ(a) int((a).size())
#define EACH(i, c)                                                             \
  for (typeof((c).begin()) i = (c).begin(); i != (c).end(); ++i)
#define EXIST(s, e) ((s).find(e) != (s).end())
#define COUNT(obj, v) count((obj).begin(), (obj).end(), v)
#define SEARCH(v, w) search((v).begin(), (v).end(), (w).begin(), (w).end())
#define B_SEARCH(obj, v) binary_search((obj).begin(), (obj).end(), v)
#define SORT(c) sort((c).begin(), (c).end())
#define RSORT(c) sort((c).rbegin(), (c).rend())
#define REVERSE(c) reverse((c).begin(), (c).end())
#define SUMI(obj) accumulate((obj).begin(), (obj).end(), 0)
#define SUMD(obj) accumulate((obj).begin(), (obj).end(), 0.)
#define SUMLL(obj) accumulate((obj).begin(), (obj).end(), 0LL)
#define SUMS(obj) accumulate((obj).begin(), (obj).end(), string())
#define SUM_P(v, w) partial_sum((v).begin(), (v).end(), (w).begin())
#define UB(obj, n) upper_bound((obj).begin(), (obj).end(), n)
#define LB(obj, n) lower_bound((obj).begin(), (obj).end(), n)
#define PB push_back
#define MP make_pair

// input output
//------------------------------------------
#define GL(s) getline(cin, (s))
#define INIT                                                                   \
  std::ios::sync_with_stdio(false);                                            \
  std::cin.tie(0);
#define OUT(d) std::cout << (d);
#define OUT_L(d) std::cout << (d) << endl;
#define FOUT(n, d) std::cout << std::fixed << std::setprecision(n) << (d);
#define FOUT_L(n, d)                                                           \
  std::cout << std::fixed << std::setprecision(n) << (d) << "\n";
#define EL() std::cout << "\n";
#define SHOW_VECTOR(v)                                                         \
  {                                                                            \
    std::cerr << #v << "\t:";                                                  \
    for (const auto &xxx : v) {                                                \
      std::cerr << xxx << " ";                                                 \
    }                                                                          \
    std::cerr << "\n";                                                         \
  }
#define SHOW_MAP(v)                                                            \
  {                                                                            \
    std::cerr << #v << endl;                                                   \
    for (const auto &xxx : v) {                                                \
      std::cerr << xxx.first << " " << xxx.second << "\n";                     \
    }                                                                          \
  }

// repetition
//------------------------------------------
#define FOR(i, a, b) for (int i = (a); i < (b); ++i)
#define RFOR(i, a, b) for (int i = (b)-1; i >= (a); --i)
#define REP(i, n) FOR(i, 0, n)
#define RREP(i, n) for (int i = n - 1; i >= 0; i--)
#define FORLL(i, a, b) for (LL i = LL(a); i < LL(b); ++i)
#define RFORLL(i, a, b) for (LL i = LL(b) - 1; i >= LL(a); --i)
#define REPLL(i, n) for (LL i = 0; i < LL(n); ++i)
#define RREPLL(i, n) for (LL i = LL(n) - 1; i >= 0; --i)
#define FOREACH(x, v) for (auto &(x) : (v))
#define FORITER(x, v) for (auto(x) = (v).begin(); (x) != (v).end(); ++(x))

// constant
//--------------------------------------------
const double EPS = 1e-10;
const double PI = acos(-1.0);
const int MOD = 1000000007;

// math
//--------------------------------------------

// min <= aim <= max
template <typename T>
inline bool BETWEEN(const T aim, const T min, const T max) {
  if (min <= aim && aim <= max) {
    return true;
  } else {
    return false;
  }
}

template <class T> inline T SQR(const T x) { return x * x; }

template <class T1, class T2> inline T1 POW(const T1 x, const T2 y) {
  if (!y)
    return 1;
  else if ((y & 1) == 0) {
    return SQR(POW(x, y >> 1));
  } else
    return POW(x, y ^ 1) * x;
}

template <typename T> constexpr T ABS(T x) {
  static_assert(is_signed<T>::value, "ABS(): argument must be signed");
  return x < 0 ? -x : x;
}

// partial_permutation nPr 順列
// first・・最初の数
// middle・・r(取り出す数)
// last・・n(全体数)
template <class BidirectionalIterator>
bool next_partial_permutation(BidirectionalIterator first,
                              BidirectionalIterator middle,
                              BidirectionalIterator last) {
  reverse(middle, last);
  return next_permutation(first, last);
}

// combination nCr 組み合わせ
// first1・・最初の数
// last1==first2・・r(取り出す数)
// last2・・n(全体数)
template <class BidirectionalIterator>
bool next_combination(BidirectionalIterator first1, BidirectionalIterator last1,
                      BidirectionalIterator first2,
                      BidirectionalIterator last2) {
  if ((first1 == last1) || (first2 == last2)) {
    return false;
  }
  BidirectionalIterator m1 = last1;
  BidirectionalIterator m2 = last2;
  --m2;
  while (--m1 != first1 && !(*m1 < *m2)) {
  }
  bool result = (m1 == first1) && !(*first1 < *m2);
  if (!result) {
    while (first2 != m2 && !(*m1 < *first2)) {
      ++first2;
    }
    first1 = m1;
    std::iter_swap(first1, first2);
    ++first1;
    ++first2;
  }
  if ((first1 != last1) && (first2 != last2)) {
    m1 = last1;
    m2 = first2;
    while ((m1 != first1) && (m2 != last2)) {
      std::iter_swap(--m1, m2);
      ++m2;
    }
    std::reverse(first1, m1);
    std::reverse(first1, last1);
    std::reverse(m2, last2);
    std::reverse(first2, last2);
  }
  return !result;
}

// numeric_law
//--------------------------------------------

template <typename T> constexpr bool ODD(T x) { return x % 2 != 0; }

template <typename T> constexpr bool EVEN(T x) { return x % 2 == 0; }

// 最大公約数
template <class T> inline T GCD(const T x, const T y) {
  if (x < 0)
    return GCD(-x, y);
  if (y < 0)
    return GCD(x, -y);
  return (!y) ? x : GCD(y, x % y);
}

// 最小公倍数
template <class T> inline T LCM(const T x, const T y) {
  if (x < 0)
    return LCM(-x, y);
  if (y < 0)
    return LCM(x, -y);
  return x * (y / GCD(x, y));
}

// ax + by = 1
// x,yが変数に格納される
template <class T> inline T EXTGCD(const T a, const T b, T &x, T &y) {
  if (a < 0) {
    T d = EXTGCD(-a, b, x, y);
    x = -x;
    return d;
  }
  if (b < 0) {
    T d = EXTGCD(a, -b, x, y);
    y = -y;
    return d;
  }
  if (!b) {
    x = 1;
    y = 0;
    return a;
  } else {
    T d = EXTGCD(b, a % b, x, y);
    T t = x;
    x = y;
    y = t - (a / b) * y;
    return d;
  }
}

// 素数
template <class T> inline bool ISPRIME(const T x) {
  if (x <= 1)
    return false;
  for (T i = 2; SQR(i) <= x; i++)
    if (x % i == 0)
      return false;
  return true;
}

// 素数をtrueとして返す
template <class T> VB ERATOSTHENES(const T n) {
  VB arr(n, true);
  for (int i = 2; SQR(i) < n; i++) {
    if (arr[i]) {
      for (int j = 0; i * (j + 2) < n; j++) {
        arr[i * (j + 2)] = false;
      }
    }
  }
  return arr;
}

// a <= x < b の素数を返す
template <typename T> VB ERATOSTHENES(const T a, const T b) {
  VB small = ERATOSTHENES(b);
  VB prime(b - a, true);

  for (int i = 2; (T)(SQR(i)) < b; i++) {
    if (small[i]) {
      for (T j = max(2, (a + i - 1) / i) * i; j < b; j += i) {
        prime[j - a] = false;
      }
    }
  }

  return prime;
}

// 約数
template <class T> vector<T> DIVISOR(T n) {
  vector<T> v;
  for (int i = 1; i * i <= n; ++i) {
    if (n % i == 0) {
      v.push_back(i);
      if (i != n / i) {
        v.push_back(n / i);
      }
    }
  }
  sort(v.begin(), v.end());
  return v;
}

// 組み合わせ個数
template <typename T> T NCR(T n, T r) {
  T ans = 1;
  for (T i = n; i > n - r; --i) {
    ans = ans * i;
  }
  for (T i = 1; i < r + 1; ++i) {
    ans = ans / i;
  }
  return ans;
}

// 行列
int MATRIZ_CHAIN(VI &p, VVI &s) {
  const static int INF = 1 << 20;
  const int n = p.size() - 1;
  VVI X(n, VI(n, INF));
  s.resize(n, VI(n));
  for (int i = 0; i < n; ++i)
    X[i][i] = 0;
  for (int w = 1; w < n; ++w)
    for (int i = 0, j; j = i + w, j < n; ++i)
      for (int k = i; k < j; ++k) {
        int f = p[i] * p[k + 1] * p[j + 1];
        if (X[i][k] + X[k + 1][j] + f < X[i][j]) {
          X[i][j] = X[i][k] + X[k + 1][j] + f;
          s[i][j] = k;
        }
      }
  return X[0][n - 1];
}

// 最長増加部分列
VI LIS(const VI &a) {
  const static int INF = 99999999;
  const int n = a.size();
  VI A(n, INF);
  VI id(n);
  for (int i = 0; i < n; ++i) {
    id[i] = distance(A.begin(), lower_bound(A.begin(), A.end(), a[i]));
    A[id[i]] = a[i];
  }
  int m = *max_element(id.begin(), id.end());
  VI b(m + 1);
  for (int i = n - 1; i >= 0; --i)
    if (id[i] == m)
      b[m--] = a[i];
  return b;
}

// 最長共通部分列 string->toVC
template <typename T> vector<T> LCS(const vector<T> &a, const vector<T> &b) {
  const int n = a.size(), m = b.size();
  vector<VI> X(n + 1, VI(m + 1));
  vector<VI> Y(n + 1, VI(m + 1));
  REP(i, n) {
    REP(j, m) {
      if (a[i] == b[j]) {
        X[i + 1][j + 1] = X[i][j] + 1;
        Y[i + 1][j + 1] = 0;
      } else if (X[i + 1][j] < X[i][j + 1]) {
        X[i + 1][j + 1] = X[i][j + 1];
        Y[i + 1][j + 1] = +1;
      } else {
        X[i + 1][j + 1] = X[i + 1][j];
        Y[i + 1][j + 1] = -1;
      }
    }
  }
  vector<T> c;
  for (int i = n, j = m; i > 0 && j > 0;) {
    if (Y[i][j] > 0)
      --i;
    else if (Y[i][j] < 0)
      --j;
    else {
      c.PB(a[i - 1]);
      --i;
      --j;
    }
  }
  REVERSE(c);
  return c;
}

// コイン C総額 cs使用できるコインの種類
VI money_change(int C, VI &cs) {
  const int INF = 99999999;
  int n = cs.size();
  VI xs(C + 1, INF);
  VI ys(C + 1);
  xs[0] = 0;
  for (int i = 0; i < n; ++i) {
    for (int c = 0; c + cs[i] <= C; ++c) {
      if (xs[c + cs[i]] > xs[c] + 1) {
        xs[c + cs[i]] = xs[c] + 1;
        ys[c + cs[i]] = c;
      }
    }
  }
  VI zs;
  for (int c = C; c > 0; c = ys[c]) {
    zs.push_back(c - ys[c]);
  }
  return zs;
}

// confirmation
//--------------------------------------------

// clear memory
#define CLR(a, b) memset((a), (b), sizeof(a))

// debug
#define dump(x) cerr << #x << " = " << (x) << endl;
#define debug(x)                                                               \
  cerr << #x << " = " << (x) << " (L" << __LINE__ << ")"                       \
       << " " << __FILE__ << endl;

/*
 *
 *
 *   ~~~~Below My Answer~~~~
 *
 *
 * */

// 素集合データ構造
//--------------------------------------------
struct UnionFind {

  // par[i]→データiの親の番号 i==par[i]ならiは木の親
  vector<int> par;
  // sizes[i]→iを根とする木に含まれる子の数
  vector<int> sizes;

  UnionFind(int n) : par(n), sizes(n, 1) {
    // すべてのノードがiに属すると初期化
    REP(i, n) { par[i] = i; }
  }

  // データxが属する木の根を得る
  int find(int x) {
    if (x == par[x]) {
      return x;
    }
    return par[x] = find(par[x]);
  }

  // 2つのデータx, yが属する木をマージする
  void unite(int x, int y) {
    // データの根ノードを得る
    x = find(x);
    y = find(y);

    // 同じ木ならマージしない
    if (x == y) {
      return;
    }

    // xの木 > yの木
    if (sizes[x] < sizes[y]) {
      swap(x, y);
    }
    // xはyの親とする
    par[y] = x;
    sizes[x] += sizes[y];
  }

  // x,yが同じ木ならtrue
  bool same(int x, int y) { return find(x) == find(y); }

  // xが含まれる木のサイズ
  int size(int x) { return sizes[find(x)]; }
};

int main() {

  int N, M;
  cin >> N >> M;

  VI p(N);
  REP(i, N) { cin >> p[i]; }

  vector<PII> xy(N);
  REP(i, M) {
    int x, y;
    cin >> x >> y;
    xy[i] = MP(x, y);
  }

  UnionFind uf = UnionFind(N);
  REP(i, M) { uf.unite(xy[i].first - 1, xy[i].second - 1); }

  int count = 0;
  REP(i, N) {
    if (p[i] == i + 1) {
      count++;
    } else {
      if (uf.same(i, p[i] - 1)) {
        count++;
      }
    }
  }

  OUT_L(count);

  return 0;
}


Fixed submission:
// include
//------------------------------------------
#include <algorithm>
#include <bitset>
#include <cctype>
#include <climits>
#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <ctime>
#include <deque>
#include <functional>
#include <iomanip>
#include <iostream>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <utility>
#include <vector>

using namespace std;

// typedef
//------------------------------------------
typedef long long LL;
typedef vector<int> VI;
typedef vector<bool> VB;
typedef vector<char> VC;
typedef vector<double> VD;
typedef vector<string> VS;
typedef vector<LL> VLL;
typedef vector<VI> VVI;
typedef vector<VB> VVB;
typedef vector<VS> VVS;
typedef vector<VLL> VVLL;
typedef vector<VVI> VVVI;
typedef pair<int, int> PII;
typedef pair<LL, LL> PLL;
typedef pair<int, string> PIS;
typedef pair<string, int> PSI;
typedef pair<string, string> PSS;

// 数値・文字列
//------------------------------------------
inline int toInt(string s) {
  int v;
  istringstream sin(s);
  sin >> v;
  return v;
}

inline LL toLongLong(string s) {
  LL v;
  istringstream sin(s);
  sin >> v;
  return v;
}

template <class T> inline string toString(T x) {
  ostringstream sout;
  sout << x;
  return sout.str();
}

inline VC toVC(string s) {
  VC data(s.begin(), s.end());
  return data;
}

template <typename List>
void SPRIT(const std::string &s, const std::string &delim, List &result) {
  result.clear();
  string::size_type pos = 0;
  while (pos != string::npos) {
    string::size_type p = s.find(delim, pos);
    if (p == string::npos) {
      result.push_back(s.substr(pos));
      break;
    } else {
      result.push_back(s.substr(pos, p - pos));
    }
    pos = p + delim.size();
  }
}

string TRIM(const string &str, const char *trimCharacterList = " \t\v\r\n") {
  string result;
  string::size_type left = str.find_first_not_of(trimCharacterList);
  if (left != string::npos) {
    string::size_type right = str.find_last_not_of(trimCharacterList);
    result = str.substr(left, right - left + 1);
  }
  return result;
}

template <typename T> bool VECTOR_EXISTS(vector<T> vec, T data) {
  auto itr = std::find(vec.begin(), vec.end(), data);
  size_t index = distance(vec.begin(), itr);
  if (index != vec.size()) {
    return true;
  } else {
    return 0;
  }
}

#define UPPER(s) transform((s).begin(), (s).end(), (s).begin(), ::toupper)
#define LOWER(s) transform((s).begin(), (s).end(), (s).begin(), ::tolower)

// 四捨五入 nLen=小数点第N位にする
//------------------------------------------

// 四捨五入
double ceil_n(double dIn, int nLen) {
  double dOut;
  dOut = dIn * pow(10.0, nLen);
  dOut = (double)(int)(dOut + 0.9);
  return dOut * pow(10.0, -nLen);
}

// 切り捨て
double floor_n(double dIn, int nLen) {
  double dOut;
  dOut = dIn * pow(10.0, nLen);
  dOut = (double)(int)(dOut);
  return dOut * pow(10.0, -nLen);
}

// 切り上げ
double round_n(double dIn, int nLen) {
  double dOut;
  dOut = dIn * pow(10.0, nLen);
  dOut = (double)(int)(dOut + 0.5);
  return dOut * pow(10.0, -nLen);
}

// n桁目の数の取得
int take_a_n(int num, int n) {
  string str = toString(num);
  return str[str.length() - n] - '0';
}

// 進数
//------------------------------------------

//"1111011" → 123
int strbase_2to10(const std::string &s) {
  int out = 0;
  for (int i = 0, size = s.size(); i < size; ++i) {
    out *= 2;
    out += ((int)s[i] == 49) ? 1 : 0;
  }
  return out;
}

//"123" → 1111011
int strbase_10to2(const std::string &s) {
  int binary = toInt(s);
  int out = 0;
  for (int i = 0; binary > 0; i++) {
    out = out + (binary % 2) * pow(static_cast<int>(10), i);
    binary = binary / 2;
  }
  return out;
}

//"ABC" 2748
int strbase_16to10(const std::string &s) {
  int out = stoi(s, 0, 16);
  return out;
}

// 1111011 → 123
int intbase_2to10(int in) {
  string str = toString(in);
  return strbase_2to10(str);
}

// 123 → 1111011
int intbase_10to2(int in) {
  string str = toString(in);
  return strbase_10to2(str);
}

int intbase_16to10(int in) {
  string str = toString(in);
  return strbase_16to10(str);
}

// 123→ "7B"
string intbase_10to16(unsigned int val, bool lower = true) {
  if (!val)
    return std::string("0");
  std::string str;
  const char hc = lower ? 'a' : 'A'; // 小文字 or 大文字表記
  while (val != 0) {
    int d = val & 15; // 16進数一桁を取得
    if (d < 10)
      str.insert(str.begin(), d + '0'); //  10未満の場合
    else                                //  10以上の場合
      str.insert(str.begin(), d - 10 + hc);
    val >>= 4;
  }
  return str;
}

// 整数を2進数表記したときの1の個数を返す
LL bitcount64(LL bits) {
  bits = (bits & 0x5555555555555555) + (bits >> 1 & 0x5555555555555555);
  bits = (bits & 0x3333333333333333) + (bits >> 2 & 0x3333333333333333);
  bits = (bits & 0x0f0f0f0f0f0f0f0f) + (bits >> 4 & 0x0f0f0f0f0f0f0f0f);
  bits = (bits & 0x00ff00ff00ff00ff) + (bits >> 8 & 0x00ff00ff00ff00ff);
  bits = (bits & 0x0000ffff0000ffff) + (bits >> 16 & 0x0000ffff0000ffff);
  return (bits & 0x00000000ffffffff) + (bits >> 32 & 0x00000000ffffffff);
}

// comparison
//------------------------------------------
#define C_MAX(a, b) ((a) > (b) ? (a) : (b))
#define C_MIN(a, b) ((a) < (b) ? (a) : (b))
#define C_ABS(a, b) ((a) < (b) ? (b) - (a) : (a) - (b))

// container util
//------------------------------------------
#define ALL(a) (a).begin(), (a).end()
#define RALL(a) (a).rbegin(), (a).rend()
#define SZ(a) int((a).size())
#define EACH(i, c)                                                             \
  for (typeof((c).begin()) i = (c).begin(); i != (c).end(); ++i)
#define EXIST(s, e) ((s).find(e) != (s).end())
#define COUNT(obj, v) count((obj).begin(), (obj).end(), v)
#define SEARCH(v, w) search((v).begin(), (v).end(), (w).begin(), (w).end())
#define B_SEARCH(obj, v) binary_search((obj).begin(), (obj).end(), v)
#define SORT(c) sort((c).begin(), (c).end())
#define RSORT(c) sort((c).rbegin(), (c).rend())
#define REVERSE(c) reverse((c).begin(), (c).end())
#define SUMI(obj) accumulate((obj).begin(), (obj).end(), 0)
#define SUMD(obj) accumulate((obj).begin(), (obj).end(), 0.)
#define SUMLL(obj) accumulate((obj).begin(), (obj).end(), 0LL)
#define SUMS(obj) accumulate((obj).begin(), (obj).end(), string())
#define SUM_P(v, w) partial_sum((v).begin(), (v).end(), (w).begin())
#define UB(obj, n) upper_bound((obj).begin(), (obj).end(), n)
#define LB(obj, n) lower_bound((obj).begin(), (obj).end(), n)
#define PB push_back
#define MP make_pair

// input output
//------------------------------------------
#define GL(s) getline(cin, (s))
#define INIT                                                                   \
  std::ios::sync_with_stdio(false);                                            \
  std::cin.tie(0);
#define OUT(d) std::cout << (d);
#define OUT_L(d) std::cout << (d) << endl;
#define FOUT(n, d) std::cout << std::fixed << std::setprecision(n) << (d);
#define FOUT_L(n, d)                                                           \
  std::cout << std::fixed << std::setprecision(n) << (d) << "\n";
#define EL() std::cout << "\n";
#define SHOW_VECTOR(v)                                                         \
  {                                                                            \
    std::cerr << #v << "\t:";                                                  \
    for (const auto &xxx : v) {                                                \
      std::cerr << xxx << " ";                                                 \
    }                                                                          \
    std::cerr << "\n";                                                         \
  }
#define SHOW_MAP(v)                                                            \
  {                                                                            \
    std::cerr << #v << endl;                                                   \
    for (const auto &xxx : v) {                                                \
      std::cerr << xxx.first << " " << xxx.second << "\n";                     \
    }                                                                          \
  }

// repetition
//------------------------------------------
#define FOR(i, a, b) for (int i = (a); i < (b); ++i)
#define RFOR(i, a, b) for (int i = (b)-1; i >= (a); --i)
#define REP(i, n) FOR(i, 0, n)
#define RREP(i, n) for (int i = n - 1; i >= 0; i--)
#define FORLL(i, a, b) for (LL i = LL(a); i < LL(b); ++i)
#define RFORLL(i, a, b) for (LL i = LL(b) - 1; i >= LL(a); --i)
#define REPLL(i, n) for (LL i = 0; i < LL(n); ++i)
#define RREPLL(i, n) for (LL i = LL(n) - 1; i >= 0; --i)
#define FOREACH(x, v) for (auto &(x) : (v))
#define FORITER(x, v) for (auto(x) = (v).begin(); (x) != (v).end(); ++(x))

// constant
//--------------------------------------------
const double EPS = 1e-10;
const double PI = acos(-1.0);
const int MOD = 1000000007;

// math
//--------------------------------------------

// min <= aim <= max
template <typename T>
inline bool BETWEEN(const T aim, const T min, const T max) {
  if (min <= aim && aim <= max) {
    return true;
  } else {
    return false;
  }
}

template <class T> inline T SQR(const T x) { return x * x; }

template <class T1, class T2> inline T1 POW(const T1 x, const T2 y) {
  if (!y)
    return 1;
  else if ((y & 1) == 0) {
    return SQR(POW(x, y >> 1));
  } else
    return POW(x, y ^ 1) * x;
}

template <typename T> constexpr T ABS(T x) {
  static_assert(is_signed<T>::value, "ABS(): argument must be signed");
  return x < 0 ? -x : x;
}

// partial_permutation nPr 順列
// first・・最初の数
// middle・・r(取り出す数)
// last・・n(全体数)
template <class BidirectionalIterator>
bool next_partial_permutation(BidirectionalIterator first,
                              BidirectionalIterator middle,
                              BidirectionalIterator last) {
  reverse(middle, last);
  return next_permutation(first, last);
}

// combination nCr 組み合わせ
// first1・・最初の数
// last1==first2・・r(取り出す数)
// last2・・n(全体数)
template <class BidirectionalIterator>
bool next_combination(BidirectionalIterator first1, BidirectionalIterator last1,
                      BidirectionalIterator first2,
                      BidirectionalIterator last2) {
  if ((first1 == last1) || (first2 == last2)) {
    return false;
  }
  BidirectionalIterator m1 = last1;
  BidirectionalIterator m2 = last2;
  --m2;
  while (--m1 != first1 && !(*m1 < *m2)) {
  }
  bool result = (m1 == first1) && !(*first1 < *m2);
  if (!result) {
    while (first2 != m2 && !(*m1 < *first2)) {
      ++first2;
    }
    first1 = m1;
    std::iter_swap(first1, first2);
    ++first1;
    ++first2;
  }
  if ((first1 != last1) && (first2 != last2)) {
    m1 = last1;
    m2 = first2;
    while ((m1 != first1) && (m2 != last2)) {
      std::iter_swap(--m1, m2);
      ++m2;
    }
    std::reverse(first1, m1);
    std::reverse(first1, last1);
    std::reverse(m2, last2);
    std::reverse(first2, last2);
  }
  return !result;
}

// numeric_law
//--------------------------------------------

template <typename T> constexpr bool ODD(T x) { return x % 2 != 0; }

template <typename T> constexpr bool EVEN(T x) { return x % 2 == 0; }

// 最大公約数
template <class T> inline T GCD(const T x, const T y) {
  if (x < 0)
    return GCD(-x, y);
  if (y < 0)
    return GCD(x, -y);
  return (!y) ? x : GCD(y, x % y);
}

// 最小公倍数
template <class T> inline T LCM(const T x, const T y) {
  if (x < 0)
    return LCM(-x, y);
  if (y < 0)
    return LCM(x, -y);
  return x * (y / GCD(x, y));
}

// ax + by = 1
// x,yが変数に格納される
template <class T> inline T EXTGCD(const T a, const T b, T &x, T &y) {
  if (a < 0) {
    T d = EXTGCD(-a, b, x, y);
    x = -x;
    return d;
  }
  if (b < 0) {
    T d = EXTGCD(a, -b, x, y);
    y = -y;
    return d;
  }
  if (!b) {
    x = 1;
    y = 0;
    return a;
  } else {
    T d = EXTGCD(b, a % b, x, y);
    T t = x;
    x = y;
    y = t - (a / b) * y;
    return d;
  }
}

// 素数
template <class T> inline bool ISPRIME(const T x) {
  if (x <= 1)
    return false;
  for (T i = 2; SQR(i) <= x; i++)
    if (x % i == 0)
      return false;
  return true;
}

// 素数をtrueとして返す
template <class T> VB ERATOSTHENES(const T n) {
  VB arr(n, true);
  for (int i = 2; SQR(i) < n; i++) {
    if (arr[i]) {
      for (int j = 0; i * (j + 2) < n; j++) {
        arr[i * (j + 2)] = false;
      }
    }
  }
  return arr;
}

// a <= x < b の素数を返す
template <typename T> VB ERATOSTHENES(const T a, const T b) {
  VB small = ERATOSTHENES(b);
  VB prime(b - a, true);

  for (int i = 2; (T)(SQR(i)) < b; i++) {
    if (small[i]) {
      for (T j = max(2, (a + i - 1) / i) * i; j < b; j += i) {
        prime[j - a] = false;
      }
    }
  }

  return prime;
}

// 約数
template <class T> vector<T> DIVISOR(T n) {
  vector<T> v;
  for (int i = 1; i * i <= n; ++i) {
    if (n % i == 0) {
      v.push_back(i);
      if (i != n / i) {
        v.push_back(n / i);
      }
    }
  }
  sort(v.begin(), v.end());
  return v;
}

// 組み合わせ個数
template <typename T> T NCR(T n, T r) {
  T ans = 1;
  for (T i = n; i > n - r; --i) {
    ans = ans * i;
  }
  for (T i = 1; i < r + 1; ++i) {
    ans = ans / i;
  }
  return ans;
}

// 行列
int MATRIZ_CHAIN(VI &p, VVI &s) {
  const static int INF = 1 << 20;
  const int n = p.size() - 1;
  VVI X(n, VI(n, INF));
  s.resize(n, VI(n));
  for (int i = 0; i < n; ++i)
    X[i][i] = 0;
  for (int w = 1; w < n; ++w)
    for (int i = 0, j; j = i + w, j < n; ++i)
      for (int k = i; k < j; ++k) {
        int f = p[i] * p[k + 1] * p[j + 1];
        if (X[i][k] + X[k + 1][j] + f < X[i][j]) {
          X[i][j] = X[i][k] + X[k + 1][j] + f;
          s[i][j] = k;
        }
      }
  return X[0][n - 1];
}

// 最長増加部分列
VI LIS(const VI &a) {
  const static int INF = 99999999;
  const int n = a.size();
  VI A(n, INF);
  VI id(n);
  for (int i = 0; i < n; ++i) {
    id[i] = distance(A.begin(), lower_bound(A.begin(), A.end(), a[i]));
    A[id[i]] = a[i];
  }
  int m = *max_element(id.begin(), id.end());
  VI b(m + 1);
  for (int i = n - 1; i >= 0; --i)
    if (id[i] == m)
      b[m--] = a[i];
  return b;
}

// 最長共通部分列 string->toVC
template <typename T> vector<T> LCS(const vector<T> &a, const vector<T> &b) {
  const int n = a.size(), m = b.size();
  vector<VI> X(n + 1, VI(m + 1));
  vector<VI> Y(n + 1, VI(m + 1));
  REP(i, n) {
    REP(j, m) {
      if (a[i] == b[j]) {
        X[i + 1][j + 1] = X[i][j] + 1;
        Y[i + 1][j + 1] = 0;
      } else if (X[i + 1][j] < X[i][j + 1]) {
        X[i + 1][j + 1] = X[i][j + 1];
        Y[i + 1][j + 1] = +1;
      } else {
        X[i + 1][j + 1] = X[i + 1][j];
        Y[i + 1][j + 1] = -1;
      }
    }
  }
  vector<T> c;
  for (int i = n, j = m; i > 0 && j > 0;) {
    if (Y[i][j] > 0)
      --i;
    else if (Y[i][j] < 0)
      --j;
    else {
      c.PB(a[i - 1]);
      --i;
      --j;
    }
  }
  REVERSE(c);
  return c;
}

// コイン C総額 cs使用できるコインの種類
VI money_change(int C, VI &cs) {
  const int INF = 99999999;
  int n = cs.size();
  VI xs(C + 1, INF);
  VI ys(C + 1);
  xs[0] = 0;
  for (int i = 0; i < n; ++i) {
    for (int c = 0; c + cs[i] <= C; ++c) {
      if (xs[c + cs[i]] > xs[c] + 1) {
        xs[c + cs[i]] = xs[c] + 1;
        ys[c + cs[i]] = c;
      }
    }
  }
  VI zs;
  for (int c = C; c > 0; c = ys[c]) {
    zs.push_back(c - ys[c]);
  }
  return zs;
}

// confirmation
//--------------------------------------------

// clear memory
#define CLR(a, b) memset((a), (b), sizeof(a))

// debug
#define dump(x) cerr << #x << " = " << (x) << endl;
#define debug(x)                                                               \
  cerr << #x << " = " << (x) << " (L" << __LINE__ << ")"                       \
       << " " << __FILE__ << endl;

/*
 *
 *
 *   ~~~~Below My Answer~~~~
 *
 *
 * */

// 素集合データ構造
//--------------------------------------------
struct UnionFind {

  // par[i]→データiの親の番号 i==par[i]ならiは木の親
  vector<int> par;
  // sizes[i]→iを根とする木に含まれる子の数
  vector<int> sizes;

  UnionFind(int n) : par(n), sizes(n, 1) {
    // すべてのノードがiに属すると初期化
    REP(i, n) { par[i] = i; }
  }

  // データxが属する木の根を得る
  int find(int x) {
    if (x == par[x]) {
      return x;
    }
    return par[x] = find(par[x]);
  }

  // 2つのデータx, yが属する木をマージする
  void unite(int x, int y) {
    // データの根ノードを得る
    x = find(x);
    y = find(y);

    // 同じ木ならマージしない
    if (x == y) {
      return;
    }

    // xの木 > yの木
    if (sizes[x] < sizes[y]) {
      swap(x, y);
    }
    // xはyの親とする
    par[y] = x;
    sizes[x] += sizes[y];
  }

  // x,yが同じ木ならtrue
  bool same(int x, int y) { return find(x) == find(y); }

  // xが含まれる木のサイズ
  int size(int x) { return sizes[find(x)]; }
};

int main() {

  int N, M;
  cin >> N >> M;

  VI p(N);
  REP(i, N) { cin >> p[i]; }

  vector<PII> xy(M);
  REP(i, M) {
    int x, y;
    cin >> x >> y;
    xy[i] = MP(x, y);
  }

  UnionFind uf = UnionFind(N);
  REP(i, M) { uf.unite(xy[i].first - 1, xy[i].second - 1); }

  int count = 0;
  REP(i, N) {
    if (p[i] == i + 1) {
      count++;
    } else {
      if (uf.same(i, p[i] - 1)) {
        count++;
      }
    }
  }

  OUT_L(count);

  return 0;
}