class UnionFind{

private:
    int* parent;
    int* rank; // rank[i]表示以i为根的集合所表示的树的层数
    int count;

public:
    UnionFind(int count){
        parent = new int[count];
        rank = new int[count];
        this->count = count;
        for( int i = 0 ; i < count ; i ++ ){
            parent[i] = i;
            rank[i] = 1;
        }
    }

    ~UnionFind(){
        delete[] parent;
        delete[] rank;
    }

    int size(){
        return count;
    }

    bool isConnected( int p , int q ){
        return find(p) == find(q);
    }

    int find(int p){
        assert( p >= 0 && p < count );
        while( p != parent[p] )
            p = parent[p];
        return p;
    }

    void unionElements(int p, int q){

        int pRoot = find(p);
        int qRoot = find(q);

        if( pRoot == qRoot )
            return;

        if( rank[pRoot] < rank[qRoot] )
            parent[pRoot] = qRoot;
        else if( rank[qRoot] < rank[pRoot])
            parent[qRoot] = pRoot;
        else{ // rank[pRoot] == rank[qRoot]
            parent[pRoot] = qRoot;
            rank[qRoot] ++;
        }
    }
};

class UnionFind{

private:
    int* parent;
    int* rank;
    int count;

public:
    UnionFind(int count){
        parent = new int[count];
        rank = new int[count];
        this->count = count;
        for( int i = 0 ; i < count ; i ++ ){
            parent[i] = i;
            rank[i] = 1;
        }
    }

    ~UnionFind(){
        delete[] parent;
        delete[] rank;
    }

    int size(){
        return count;
    }

    bool isConnected( int p , int q ){
        return find(p) == find(q);
    }

    int find(int p){

        assert( p >= 0 && p < count );

        // path compression 1
        while( p != parent[p] ){
            parent[p] = parent[parent[p]];
            p = parent[p];
        }
        return p;

        // path compression 2
//            if( p != parent[p] )
//                parent[p] = find( parent[p] );
//            return parent[p];
    }

    void unionElements(int p, int q){

        int pRoot = find(p);
        int qRoot = find(q);

        if( pRoot == qRoot )
            return;

        if( rank[pRoot] < rank[qRoot] )
            parent[pRoot] = qRoot;
        else if( rank[qRoot] < rank[pRoot])
            parent[qRoot] = pRoot;
        else{ // rank[pRoot] == rank[qRoot]
            parent[pRoot] = qRoot;
            rank[qRoot] ++;
        }

    }

    void show(){
        for( int i = 0 ; i < count ; i ++ )
            cout<<i<<" : "<<parent[i]<<endl;
    }
};