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void init() {
    for (int i = 1; i <= n; i++) f[i] = i, rk[i] = 1;
}

int find(int x) {
    if (x != f[x]) f[x] = find(f[x]);
    return f[x];
}

void merge(int x, int y) {
    x = find(x);
    y = find(y);
    if (rk[x] > rk[y])
        f[y] = x;
    else {
        f[x] = y;
        if (rk[x] == rk[y]) rk[y]++;
    }
}

bool same(int x, int y) { return find(x) == find(y); }