vector<int> uf;

init(int N) {
	uf.assign(N,-1); //-1 indicates that every subset has size 1
}

int findSet(int i) {
	if(uf[i] < 0) return i; //If uf[i] < 0 we have reach a root
	uf[i] = findSet(uf[i]); //Path-Compression
	return uf[i];
}
	
void linkSets(int i, int j) {
	//Take |uf[i]|, where i must be a root, to get the size 
	//of the subset
	if(abs(uf[i]) < abs(uf[j])) { //Union-by-size.
		uf[j] += uf[i]; uf[i] = j; 
	} else {
		uf[i] += uf[j]; uf[j] = i; 
	}
}
	
void unionSets(int i, int j) {
	if(findSet(i) != findSet(j)) linkSets(findSet(i),findSet(j));
}