mysql, @variable and if statement

guys, I follow instruction from this link

I created table like this

CREATE TABLE cities
(
  city VARCHAR(80),
  country VARCHAR(80),
  population INT
);

INSERT INTO cities VALUES ('New York', 'United States', 8175133); 
INSERT INTO cities VALUES ('Los Angeles', 'United States', 3792621); 
INSERT INTO cities VALUES ('Chicago', 'United States', 2695598); 

INSERT INTO cities VALUES ('Paris', 'France', 2181000);
INSERT INTO cities VALUES ('Marseille', 'France', 808000);
INSERT INTO cities VALUES ('Lyon', 'France', 422000);

INSERT INTO cities VALUES ('London', 'United Kingdom',  7825300);
INSERT INTO cities VALUES ('Birmingham', 'United Kingdom', 1016800);
INSERT INTO cities VALUES ('Leeds', 'United Kingdom', 770800);     

when i run this query

SELECT city, country, population
  FROM
  (SELECT city, country, population, 
              @country_rank := IF(@current_country = country, @country_rank + 1, 1) AS country_rank,
              @current_country := country 
    FROM cities
    ORDER BY country, population DESC
   ) ranked
   WHERE country_rank <= 2;

it doesn't give me 2 largest cities for each country

Is there something I missed? thanks