How to handel multiple checkbox field in the admin settings page with Settings API

add_action( 'admin_init', 'register_page_options' );

function register_page_options() {
    if (false == get_option('aicp_settings_options')) {
        add_option('aicp_settings_options');
    }

    // Add Section for option fields
    add_settings_section( 'aicp_section', __( '....text here....', 'aicp' ), 'display_section', 'aicp_settings' ); // id, title, display cb, page

    // Add Field for selecting countries for which you wanna ban ads
    add_settings_field( 'aicp_country_list', __( 'Select the countries', 'aicp' ), 'country_list_field', 'aicp_settings', 'aicp_section' ); // id, title, display cb, page, section

    // Register Settings
    register_setting( 'aicp_settings', 'aicp_settings_options', array( $this, 'validate_options' ) );
}

// now comes the section for checkbox

function country_list_field() {
    $options = get_option( 'aicp_settings_options' );

    $value = array();
    if (isset($options['country_list']) && ! empty($options['country_list'])) {
        $value = $options['country_list'];
    }

    $html="<input type="checkbox" name="aicp_settings_options[country_list][]" value="AF"". in_array('AF', $value) ? 'checked' : '' .'/> Afganistan';
    $html .= '<input type="checkbox" name="aicp_settings_options[country_list][]" value="AX"'. in_array('AX', $value) ? 'checked' : '' .'/> Aland Islands';

    echo $html;
}