int n;
// 0 is right
// 1 is left
void use_int_dfs(int index, int cur_state = 0, int cur_sum = 0) {
    if (cur_sum < 0) return;
    if (index == 2 * n) {
        if (cur_sum != 0) return;
        for (int i = 0;i < 2 * n;++i)
            cout << ((cur_state>>i&1) ? '(' : ')');
        cout << '\n';
        return;
    }
    // put ')'
    use_int_dfs(index+1, cur_state, cur_sum - 1);
    // put '('
    use_int_dfs(index+1, cur_state | (1<<index), cur_sum + 1);
}