// 并查集模板
class UnionFind {
public:
    vector<int> parent;
    vector<int> size;
    int n;
    // 当前连通分量数目
    int setCount;

public:
    UnionFind(int _n): n(_n), setCount(_n), parent(_n), size(_n, 1) {
        iota(parent.begin(), parent.end(), 0);
    }

    int findset(int x) {
        return parent[x] == x ? x : parent[x] = findset(parent[x]);
    }

    bool unite(int x, int y) {
        x = findset(x);
        y = findset(y);
        if (x == y) {
            return false;
        }
        if (size[x] < size[y]) {
            swap(x, y);
        }
        parent[y] = x;
        size[x] += size[y];
        --setCount;
        return true;
    }

    bool connected(int x, int y) {
        x = findset(x);
        y = findset(y);
        return x == y;
    }
    void isolate(int x) {
        if(x != parent[x]){
            parent[x] = x;
            size[x] = 1;
            ++setCount;
        }
    }
};