How to get points from OpenStreetMap of a certain country?

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i'm trying to get the list of all schools in my country, and after several tries i write the following query that works with no errors on http://overpass-turbo.eu:

/*
This has been generated by the overpass-turbo wizard.
The original search was:
“amenity=school”=“yes”
*/
[out:json][timeout:60];
// gather results
(
  // query part for: “amenity=school”
  node[amenity=school]({{geocodeBbox:Italia}});
  way[amenity=school]({{geocodeBbox:Italia}});
  relation[amenity=school]({{geocodeBbox:Italia}});
);
// print results
out body;
>;
out skel qt;

I used geocodeBbox to select all schools of Italy because geocodeId and geocodeArea (please refer to documentation) give me the following errors:

Error: line 10: parse error: ')' expected - '(' found.

Error: line 11: parse error: ')' expected - '(' found.

Error: line 11: parse error: ';' expected - ')' found.

Error: line 12: parse error: ')' expected - '(' found.

Error: line 12: parse error: ';' expected - ')' found.

Error: line 13: parse error: Unknown type ")"

Error: line 13: parse error: An empty query is not allowed

Error: line 13: parse error: Unknown type ";"

Error: line 15: parse error: An empty query is not allowed

Anyway the problem is that the query selects even schools that are not in Italy (for example there is a school from Croatia).

So, how to get exactly the points from a certain country?

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scai On BEST ANSWER

Anyway the problem is that the query selects even schools that are not in Italy (for example there is a school from Croatia).

That's correct. A bounding box (bbox) is a rectangle, not a polygon. Therefore it will always include a little bit more, except if you have a rectangle-shaped country that is also perfectly aligned with the given bbox ;)

Try this query instead:

[out:json][timeout:600];
// gather results
{{geocodeArea:Italia}}->.searchArea;
(
  // query part for: “amenity=school”
  node[amenity=school](area.searchArea);
  way[amenity=school](area.searchArea);
  relation[amenity=school](area.searchArea);
);
// print results
out body;
>;
out skel qt;