private static final String VERSION_13_8 = "13.8";

    private static final String VERSION_13_9 = "13.9";

    private static final String VERSION_13_10 = "13.10";

    private static final String VERSION_13_11 = "13.11";

    private static final String VERSION_13_12 = "13.12";

    private static final String VERSION_13_13 = "13.13";

    private static final String VERSION_13_14 = "13.14";

        Collections2.orderedPermutations(newArrayList(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12))
            .size());
    // 13 elements overflow an int
    assertEquals(
        Integer.MAX_VALUE,
        Collections2.orderedPermutations(newArrayList(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13))
            .size());
    // 21 elements overflow a long
    assertEquals(
        Integer.MAX_VALUE,

        Collections2.orderedPermutations(newArrayList(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12))
            .size());
    // 13 elements overflow an int
    assertEquals(
        Integer.MAX_VALUE,
        Collections2.orderedPermutations(newArrayList(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13))
            .size());
    // 21 elements overflow a long
    assertEquals(
        Integer.MAX_VALUE,

    bytesIn.writeUtf8("custom-foo")
    bytesIn.writeByte(0x0d) // Literal value (len = 13)
    bytesIn.writeUtf8("custom-header")
    bytesIn.writeByte(0x40) // Literal indexed
    bytesIn.writeByte(0x0a) // Literal name (len = 10)
    bytesIn.writeUtf8("custom-bar")
    bytesIn.writeByte(0x0d) // Literal value (len = 13)
    bytesIn.writeUtf8("custom-header")
    bytesIn.writeByte(0x40) // Literal indexed

    1L * 2 * 3 * 4 * 5 * 6 * 7 * 8 * 9 * 10 * 11 * 12 * 13,
    1L * 2 * 3 * 4 * 5 * 6 * 7 * 8 * 9 * 10 * 11 * 12 * 13 * 14,
    1L * 2 * 3 * 4 * 5 * 6 * 7 * 8 * 9 * 10 * 11 * 12 * 13 * 14 * 15,
    1L * 2 * 3 * 4 * 5 * 6 * 7 * 8 * 9 * 10 * 11 * 12 * 13 * 14 * 15 * 16,
    1L * 2 * 3 * 4 * 5 * 6 * 7 * 8 * 9 * 10 * 11 * 12 * 13 * 14 * 15 * 16 * 17,
    1L * 2 * 3 * 4 * 5 * 6 * 7 * 8 * 9 * 10 * 11 * 12 * 13 * 14 * 15 * 16 * 17 * 18,

    final ArrayList<Integer> initial = Lists.newArrayList(1, 15, 13, 8, 9, 10, 11, 14);
    MinMaxPriorityQueue<Integer> q = MinMaxPriorityQueue.create(initial);
    assertIntact(q);
    q.remove(9);
    q.remove(11);
    q.remove(10);
    // Now we're in the critical state: [1, 15, 13, 8, 14]
    // Removing 8 while iterating caused duplicates in iteration result.

    final ArrayList<Integer> initial = Lists.newArrayList(1, 15, 13, 8, 9, 10, 11, 14);
    MinMaxPriorityQueue<Integer> q = MinMaxPriorityQueue.create(initial);
    assertIntact(q);
    q.remove(9);
    q.remove(11);
    q.remove(10);
    // Now we're in the critical state: [1, 15, 13, 8, 14]
    // Removing 8 while iterating caused duplicates in iteration result.

## Импорт Path

Сначала импортируйте `Path` из `fastapi`, а также импортируйте `Annotated`:

=== "Python 3.10+"

    ```Python hl_lines="1  3"
    {!> ../../../docs_src/path_params_numeric_validations/tutorial001_an_py310.py!}
    ```

=== "Python 3.9+"

    ```Python hl_lines="1  3"
    {!> ../../../docs_src/path_params_numeric_validations/tutorial001_an_py39.py!}
    ```

=== "Python 3.8+"

        multimap.putAll("foo", asList(6));
        multimap.putAll("baz", asList(7, 8));
        multimap.putAll("dog", asList(9));
        multimap.putAll("bar", asList(10, 11));
        multimap.putAll("cat", asList(12, 13, 14));
        return multimap.keySet().iterator();
      }

      @Override
      protected void verify(List<String> elements) {
        assertEquals(newHashSet(elements), multimap.keySet());
      }

=== "Python 3.10+ Pydantic v2"

    ```Python hl_lines="13-24"
    {!> ../../../docs_src/schema_extra_example/tutorial001_py310.py!}
    ```

=== "Python 3.10+ Pydantic v1"

    ```Python hl_lines="13-23"
    {!> ../../../docs_src/schema_extra_example/tutorial001_py310_pv1.py!}
    ```

=== "Python 3.8+ Pydantic v2"