#include <bits/stdc++.h>
using namespace std;

#define rep(i,n) for(long long i = 0; i < (long long)(n); i++)
#define repi(i,a,b) for(long long i = (long long)(a); i < (long long)(b); i++)
#define pb push_back
#define all(x) (x).begin(), (x).end()
#define fi first
#define se second
#define mt make_tuple
#define mp make_pair
template<class T1, class T2> bool chmin(T1 &a, T2 b) { return b < a && (a = b, true); }
template<class T1, class T2> bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); }

using ll = long long; using ld = long double; using vll = vector<ll>; using vvll = vector<vll>; using vld = vector<ld>; 
using vi = vector<int>; using vvi = vector<vi>;
vll conv(vi& v) { vll r(v.size()); rep(i, v.size()) r[i] = v[i]; return r; }
using P = pair<ll, ll>;

template <typename T, typename U> ostream &operator<<(ostream &o, const pair<T, U> &v) {  o << "(" << v.first << ", " << v.second << ")"; return o; }
template<size_t...> struct seq{}; template<size_t N, size_t... Is> struct gen_seq : gen_seq<N-1, N-1, Is...>{}; template<size_t... Is> struct gen_seq<0, Is...> : seq<Is...>{};
template<class Ch, class Tr, class Tuple, size_t... Is>
void print_tuple(basic_ostream<Ch,Tr>& os, Tuple const& t, seq<Is...>){ using s = int[]; (void)s{0, (void(os << (Is == 0? "" : ", ") << get<Is>(t)), 0)...}; }
template<class Ch, class Tr, class... Args> 
auto operator<<(basic_ostream<Ch, Tr>& os, tuple<Args...> const& t) -> basic_ostream<Ch, Tr>& { os << "("; print_tuple(os, t, gen_seq<sizeof...(Args)>()); return os << ")"; }
ostream &operator<<(ostream &o, const vvll &v) { rep(i, v.size()) { rep(j, v[i].size()) o << v[i][j] << " "; cout << endl; } return o; }
template <typename T> ostream &operator<<(ostream &o, const vector<T> &v) { o << '['; rep(i, v.size()) o << v[i] << (i != v.size()-1 ? ", " : ""); o << "]";  return o; }
template <typename T>  ostream &operator<<(ostream &o, const set<T> &m) { o << '['; for (auto it = m.begin(); it != m.end(); it++) o << *it << (next(it) != m.end() ? ", " : ""); o << "]";  return o; }
template <typename T, typename U>  ostream &operator<<(ostream &o, const map<T, U> &m) { o << '['; for (auto it = m.begin(); it != m.end(); it++) o << *it << (next(it) != m.end() ? ", " : ""); o << "]";  return o; }
template <typename T, typename U>  ostream &operator<<(ostream &o, const unordered_map<T, U> &m) { o << '['; for (auto it = m.begin(); it != m.end(); it++) o << *it; o << "]";  return o; }
void printbits(ll mask, ll n) { rep(i, n) { cout << !!(mask & (1ll << i)); } cout << endl; }
#define ldout fixed << setprecision(40) 

static const double EPS = 1e-14;
static const long long INF = 1e18;
static const long long mo = 1e9+7;

struct UnionFind {
    vector<int> data;
    UnionFind(int size) : data(size, -1) { }
    // x, y????????????
    bool unite(int x, int y) {
        x = root(x); y = root(y);
        if (x != y) {
            if (data[y] < data[x]) swap(x, y);
            data[x] += data[y]; data[y] = x;
        }
        return x != y;
    }
    // x, y?????????????????????1
    bool find(int x, int y) {
        return root(x) == root(y);
    }
    // x???????????¢??????????????????????????????????????°???
    int root(int x) {
        return data[x] < 0 ? x : data[x] = root(data[x]);
    }
    // x??????????????????????????§???????????????
    int size(int x) {
        return -data[root(x)];
    }
    // ?????¢??????????????????????????°?????????
    int setNum(void) {
        map<int, int> c;
        rep(i, data.size()) {
            c[root(i)]++;
        }
        return c.size();
    }
    vector<vector<int>> getUnionList(void) {
        map<int, vector<int>> c;
        for (int i = 0; i < data.size(); i++) 
            c[root(i)].pb(i);
        vector<vector<int>> v;
        for (auto x : c) 
            v.push_back(x.second);
        return v;
    }
    void print(void) {
        auto c = getUnionList();
        for (auto x : c) {
            for (auto y : x) 
                cout << y << " ";
            cout << endl;
        }
    }
};
int main(void) {
    cin.tie(0); ios::sync_with_stdio(false);
    ll n, nx, ny; cin >> n >> nx >> ny;
    vector<P> s(n);
    
    vll rx(nx, -1), ry(ny, -1);
    bool is_wall = 0;
    rep(i, n) {
        cin >> s[i].fi >> s[i].se; s[i].fi--; s[i].se--;
        rx[s[i].fi] = ry[s[i].se] = i;
        is_wall |= (s[i].fi == 0 || s[i].fi == nx-1 || s[i].se == 0 || s[i].se == ny-1);
    }

    UnionFind uf(n);
    rep(i, n) {
        uf.unite(i, rx[s[i].fi]);
        uf.unite(i, ry[s[i].se]);
    }

    auto list = uf.getUnionList();
    if (list.size() == 1) {
        cout << (*list.begin()).size() - 1 << endl;
        return 0;
    }

    ll ret = 0;
    for (auto x : list) 
        ret += x.size() - 1;
    cout << ret + 2 * list.size() - is_wall - 1 << endl;

    return 0;
}
### Prompt

In CPP, your task is to solve the following problem:

There is a grid of size W × H surrounded by walls. Some cells in the grid are occupied by slimes. The slimes want to unite with each other and become a "King Slime".

In each move, a slime can move to east, west, south and north direction until it enters a cell occupied by another slime or hit the surrounding wall. If two slimes come together, they unite and become a new slime.

Your task is write a program which calculates the minimum number of moves that all the slimes unite and become a King Slime. Suppose slimes move one by one and they never move simultaneously.



Input

The first line contains three integers N (2 ≤ N ≤ 40,000), W and H (1 ≤ W, H ≤ 100,000), which denote the number of slimes, the width and the height of the grid respectively.

The following N lines describe the initial coordinates of the slimes. The i-th line contains two integers xi (1 ≤ xi ≤ W) and yi (1 ≤ yi ≤ H), which indicate the coordinates of the i-th slime . All the coordinates are 1-based.

You may assume that each cell is occupied by at most one slime initially.

Output

Output the minimum number of moves that all the slimes unite and become a King Slime.

Examples

Input

4 3 3
1 1
1 3
3 1
3 3


Output

3


Input

2 3 3
2 2
3 3


Output

2


Input

2 4 4
2 2
3 3


Output

3


Input

2 4 4
2 2
2 3


Output

1

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;

#define rep(i,n) for(long long i = 0; i < (long long)(n); i++)
#define repi(i,a,b) for(long long i = (long long)(a); i < (long long)(b); i++)
#define pb push_back
#define all(x) (x).begin(), (x).end()
#define fi first
#define se second
#define mt make_tuple
#define mp make_pair
template<class T1, class T2> bool chmin(T1 &a, T2 b) { return b < a && (a = b, true); }
template<class T1, class T2> bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); }

using ll = long long; using ld = long double; using vll = vector<ll>; using vvll = vector<vll>; using vld = vector<ld>; 
using vi = vector<int>; using vvi = vector<vi>;
vll conv(vi& v) { vll r(v.size()); rep(i, v.size()) r[i] = v[i]; return r; }
using P = pair<ll, ll>;

template <typename T, typename U> ostream &operator<<(ostream &o, const pair<T, U> &v) {  o << "(" << v.first << ", " << v.second << ")"; return o; }
template<size_t...> struct seq{}; template<size_t N, size_t... Is> struct gen_seq : gen_seq<N-1, N-1, Is...>{}; template<size_t... Is> struct gen_seq<0, Is...> : seq<Is...>{};
template<class Ch, class Tr, class Tuple, size_t... Is>
void print_tuple(basic_ostream<Ch,Tr>& os, Tuple const& t, seq<Is...>){ using s = int[]; (void)s{0, (void(os << (Is == 0? "" : ", ") << get<Is>(t)), 0)...}; }
template<class Ch, class Tr, class... Args> 
auto operator<<(basic_ostream<Ch, Tr>& os, tuple<Args...> const& t) -> basic_ostream<Ch, Tr>& { os << "("; print_tuple(os, t, gen_seq<sizeof...(Args)>()); return os << ")"; }
ostream &operator<<(ostream &o, const vvll &v) { rep(i, v.size()) { rep(j, v[i].size()) o << v[i][j] << " "; cout << endl; } return o; }
template <typename T> ostream &operator<<(ostream &o, const vector<T> &v) { o << '['; rep(i, v.size()) o << v[i] << (i != v.size()-1 ? ", " : ""); o << "]";  return o; }
template <typename T>  ostream &operator<<(ostream &o, const set<T> &m) { o << '['; for (auto it = m.begin(); it != m.end(); it++) o << *it << (next(it) != m.end() ? ", " : ""); o << "]";  return o; }
template <typename T, typename U>  ostream &operator<<(ostream &o, const map<T, U> &m) { o << '['; for (auto it = m.begin(); it != m.end(); it++) o << *it << (next(it) != m.end() ? ", " : ""); o << "]";  return o; }
template <typename T, typename U>  ostream &operator<<(ostream &o, const unordered_map<T, U> &m) { o << '['; for (auto it = m.begin(); it != m.end(); it++) o << *it; o << "]";  return o; }
void printbits(ll mask, ll n) { rep(i, n) { cout << !!(mask & (1ll << i)); } cout << endl; }
#define ldout fixed << setprecision(40) 

static const double EPS = 1e-14;
static const long long INF = 1e18;
static const long long mo = 1e9+7;

struct UnionFind {
    vector<int> data;
    UnionFind(int size) : data(size, -1) { }
    // x, y????????????
    bool unite(int x, int y) {
        x = root(x); y = root(y);
        if (x != y) {
            if (data[y] < data[x]) swap(x, y);
            data[x] += data[y]; data[y] = x;
        }
        return x != y;
    }
    // x, y?????????????????????1
    bool find(int x, int y) {
        return root(x) == root(y);
    }
    // x???????????¢??????????????????????????????????????°???
    int root(int x) {
        return data[x] < 0 ? x : data[x] = root(data[x]);
    }
    // x??????????????????????????§???????????????
    int size(int x) {
        return -data[root(x)];
    }
    // ?????¢??????????????????????????°?????????
    int setNum(void) {
        map<int, int> c;
        rep(i, data.size()) {
            c[root(i)]++;
        }
        return c.size();
    }
    vector<vector<int>> getUnionList(void) {
        map<int, vector<int>> c;
        for (int i = 0; i < data.size(); i++) 
            c[root(i)].pb(i);
        vector<vector<int>> v;
        for (auto x : c) 
            v.push_back(x.second);
        return v;
    }
    void print(void) {
        auto c = getUnionList();
        for (auto x : c) {
            for (auto y : x) 
                cout << y << " ";
            cout << endl;
        }
    }
};
int main(void) {
    cin.tie(0); ios::sync_with_stdio(false);
    ll n, nx, ny; cin >> n >> nx >> ny;
    vector<P> s(n);
    
    vll rx(nx, -1), ry(ny, -1);
    bool is_wall = 0;
    rep(i, n) {
        cin >> s[i].fi >> s[i].se; s[i].fi--; s[i].se--;
        rx[s[i].fi] = ry[s[i].se] = i;
        is_wall |= (s[i].fi == 0 || s[i].fi == nx-1 || s[i].se == 0 || s[i].se == ny-1);
    }

    UnionFind uf(n);
    rep(i, n) {
        uf.unite(i, rx[s[i].fi]);
        uf.unite(i, ry[s[i].se]);
    }

    auto list = uf.getUnionList();
    if (list.size() == 1) {
        cout << (*list.begin()).size() - 1 << endl;
        return 0;
    }

    ll ret = 0;
    for (auto x : list) 
        ret += x.size() - 1;
    cout << ret + 2 * list.size() - is_wall - 1 << endl;

    return 0;
}
```