//并查集 + 路径压缩 O(logn)
int fa[N];
void init(int n) { for (int i = 0; i <= n; i++) { fa[i] = i; } }
int findfa(int n) { return n == fa[n] ? n : fa[n] = findfa(fa[n]); }
inline void unite(int x, int y) {
  x = findfa(x); y = findfa(y);
  if (x != y) { fa[y] = x; }
}
//并查集 + 路径压缩 + 启发式合并 O(alpha(n))
int fa[N], rnk[N];
void init(int n) { for (int i = 0; i <= n; i++) { fa[i] = i; rnk[i] = 0; } }
int findfa(int n) { return n == fa[n] ? n : fa[n] = findfa(fa[n]); }
inline void unite(int x, int y) {
  x = findfa(x); y = findfa(y);
  if (x != y) {
    if (rnk[x] > rnk[y]) { fa[y] = x; }
    else { fa[x] = y; if (rnk[x] == rnk[y]) { rnk[y]++; } }
  }
}
//迭代路径压缩
int findfa(int n) { while (fa[n] != n) { fa[n] = fa[fa[n]]; n = fa[n]; } return n; }