while (lower <= upper) {
      int middle = (lower + upper) >>> 1;
      int c = comparator.compare(key, list.get(middle));
      if (c < 0) {
        upper = middle - 1;
      } else if (c > 0) {
        lower = middle + 1;
      } else {
        return lower
            + presentBehavior.resultIndex(
                comparator, key, list.subList(lower, upper + 1), middle - lower);
      }
    }

    while (lower <= upper) {
      int middle = (lower + upper) >>> 1;
      int c = comparator.compare(key, list.get(middle));
      if (c < 0) {
        upper = middle - 1;
      } else if (c > 0) {
        lower = middle + 1;
      } else {
        return lower
            + presentBehavior.resultIndex(
                comparator, key, list.subList(lower, upper + 1), middle - lower);
      }
    }

  private M multimap;

  protected M multimap() {
    return multimap;
  }

  /**
   * @return an array of the proper size with {@code null} as the key of the middle element.
   */
  protected Entry<K, V>[] createArrayWithNullKey() {
    Entry<K, V>[] array = createSamplesArray();
    int nullKeyLocation = getNullLocation();
    Entry<K, V> oldEntry = array[nullKeyLocation];

    for (V element : elements) {
      assertFalse("Should not contain value " + element, getMap().containsValue(element));
    }
  }

  /** @return an array of the proper size with {@code null} as the key of the middle element. */
  protected Entry<K, V>[] createArrayWithNullKey() {
    Entry<K, V>[] array = createSamplesArray();
    int nullKeyLocation = getNullLocation();
    Entry<K, V> oldEntry = array[nullKeyLocation];

    for (V element : elements) {
      assertFalse("Should not contain value " + element, getMap().containsValue(element));
    }
  }

  /** @return an array of the proper size with {@code null} as the key of the middle element. */
  protected Entry<K, V>[] createArrayWithNullKey() {
    Entry<K, V>[] array = createSamplesArray();
    int nullKeyLocation = getNullLocation();
    Entry<K, V> oldEntry = array[nullKeyLocation];

    assertEquals("Should be able to peek() at middle element", "B", peekingIterator.peek());
    assertEquals(
        "Should be able to peek() middle element multiple times", "B", peekingIterator.peek());
    assertEquals(
        "next() should still return middle element after peeking", "B", peekingIterator.next());

    assertEquals("Should be able to peek() at middle element", "B", peekingIterator.peek());
    assertEquals(
        "Should be able to peek() middle element multiple times", "B", peekingIterator.peek());
    assertEquals(
        "next() should still return middle element after peeking", "B", peekingIterator.next());

<img src="/img/tutorial/extending-openapi/image03.png">

## Change the Theme

The same way you could set the syntax highlighting theme with the key `"syntaxHighlight.theme"` (notice that it has a dot in the middle):

{* ../../docs_src/configure_swagger_ui/tutorial002.py hl[3] *}

That configuration would change the syntax highlighting color theme:

<img src="/img/tutorial/extending-openapi/image04.png">

  transform: rotate(135deg);
  -webkit-transform: rotate(135deg);
}

.daterangepicker .calendar-table th, .daterangepicker .calendar-table td {
  white-space: nowrap;
  text-align: center;
  vertical-align: middle;
  min-width: 32px;
  width: 32px;
  height: 24px;
  line-height: 24px;
  font-size: 12px;
  border-radius: 4px;
  border: 1px solid transparent;
  white-space: nowrap;
  cursor: pointer;
}

///

So, you should be able to pin to a version like:

```txt
fastapi>=0.45.0,<0.46.0
```

Breaking changes and new features are added in "MINOR" versions.

/// tip

The "MINOR" is the number in the middle, for example, in `0.2.3`, the MINOR version is `2`.

///

## Upgrading the FastAPI versions

You should add tests for your app.