private function build_next_sitemap_index_of_type( $index_type, $next_type, $state ) {
    $sitemap_type = jp_sitemap_child_type_of( $index_type );

    // If only 0 or 1 sitemaps were built, advance to the next type and return.
    if ( 1 >= $state['max'][ $sitemap_type ]['number'] ) {
      Jetpack_Sitemap_State::check_in(
        array(
          'sitemap-type'  => $next_type,
          'last-added'    => 0,
          'number'        => 0,
          'last-modified' => '1970-01-01 00:00:00',
        )
      );

      if ( $this->logger ) {
        $this->logger->report( "-- Cleaning Up $index_type" );
      }

      // There are no indices of this type.
      $this->librarian->delete_numbered_sitemap_rows_after(
        0,
        $index_type
      );

      return;
    }

    // Otherwise, try to build a sitemap index.
    $result = $this->build_one_sitemap_index(
      $state['number'] + 1,
      $state['last-added'],
      $state['last-modified'],
      $index_type
    );

    // If no index was built, advance to the next type and return.
    if ( false === $result ) {
      Jetpack_Sitemap_State::check_in(
        array(
          'sitemap-type'  => $next_type,
          'last-added'    => 0,
          'number'        => 0,
          'last-modified' => '1970-01-01 00:00:00',
        )
      );

      if ( $this->logger ) {
        $this->logger->report( "-- Cleaning Up $index_type" );
      }

      // Clean up old files.
      $this->librarian->delete_numbered_sitemap_rows_after(
        $state['number'],
        $index_type
      );

      return;
    }

    // Otherwise, check in the state.
    Jetpack_Sitemap_State::check_in(
      array(
        'sitemap-type'  => $index_type,
        'last-added'    => $result['last_id'],
        'number'        => $state['number'] + 1,
        'last-modified' => $result['last_modified'],
      )
    );

    // If there are still sitemaps left to index, return.
    if ( true === $result['any_left'] ) {
      return;
    }

    // Otherwise, advance to the next type.
    Jetpack_Sitemap_State::check_in(
      array(
        'sitemap-type'  => $next_type,
        'last-added'    => 0,
        'number'        => 0,
        'last-modified' => '1970-01-01 00:00:00',
      )
    );

    if ( $this->logger ) {
      $this->logger->report( "-- Cleaning Up $index_type" );
    }

    // We're done generating indices of this type.
    $this->librarian->delete_numbered_sitemap_rows_after(
      $state['number'] + 1,
      $index_type
    );
  }