long result = 1;
      for (int i = n1 + 1; i <= n2; i++) {
        result *= i;
      }
      return BigInteger.valueOf(result);
    }

    /*
     * We want each multiplication to have both sides with approximately the same number of digits.
     * Currently, we just divide the range in half.
     */
    int mid = (n1 + n2) >>> 1;

<img src="/img/tutorial/sub-applications/image02.png">

If you try interacting with any of the two user interfaces, they will work correctly, because the browser will be able to talk to each specific app or sub-app.

### Technical Details: `root_path` { #technical-details-root-path }

		// Unlock the 1st lock; ref=1 after this line
		nsLk.unlock("volume", "path", false)

		// Taking another lockMapMutex here allows queuing up additional lockers. This should
		// not be required but makes reproduction much easier.
		nsLk.lockMapMutex.Lock()

		// lk3 blocks.
		lk3ch := make(chan bool)
		go func() {
			lk3ch <- nsLk.lock(ctx, "volume", "path", "source", "opsID", false, 0)
		}()

		// lk4, blocks.

import org.codelibs.fess.crawler.helper.MimeTypeHelper;

import jakarta.annotation.Resource;

/**
 * An abstract base class for implementing Extractor interfaces.
 * Provides common functionality such as access to CrawlerContainer components
 * and registration with the ExtractorFactory.
 *
 * <p>
 * This class handles the retrieval of essential crawler components like

Sie sollte wie eine normale FastAPI-*Pfadoperation* aussehen:

* Sie sollte wahrscheinlich eine Deklaration des Bodys enthalten, die sie erhalten soll, z. B. `body: InvoiceEvent`.
* Und sie könnte auch eine Deklaration der Response enthalten, die zurückgegeben werden soll, z. B. `response_model=InvoiceEventReceived`.

{* ../../docs_src/openapi_callbacks/tutorial001.py hl[16:18,21:22,28:32] *}

	ctx := newContext(r, w, "KMSListKeys")
	defer logger.AuditLog(ctx, w, r, mustGetClaimsFromToken(r))

	// This only checks if the action (kms:ListKeys) is allowed, it does not check
	// each key name against the policy's Resources. We check that below, once
	// we have the list of key names from the KMS.
	objectAPI, _ := validateAdminReq(ctx, w, r, policy.KMSListKeysAction)
	if objectAPI == nil {
		return
	}

diagnostics help ensure that the underlying infrastructure that runs MinIO is configured correctly, and is functioning properly. This test is one-shot long running one, that is recommended to be run as soon as the cluster is first provisioned, and each time a failure scenario is encountered. Note that the test incurs majority of the available resources on the system. Care must be taken when using this to debug failure scenario, so as to prevent larger outages. Health tests can be triggered using...

  /**
   * The reason why this stream was closed, or null if it closed normally or has not yet been
   * closed.
   *
   * If there are multiple reasons to abnormally close this stream (such as both peers closing it
   * near-simultaneously) then this is the first reason known to this peer.
   */
  internal var errorCode: ErrorCode? = null
    get() = withLock { field }

  /**
   * This is a less carefully-controlled version of {@link #testRemovalNotification_clear} - this is
   * a black-box test that tries to create lots of different thread-interleavings, and asserts that
   * each computation is affected by a call to {@code clear()} (and therefore gets passed to the
   * removal listener), or else is not affected by the {@code clear()} (and therefore exists in the
   * cache afterward).
   */

  /**
   * This is a less carefully-controlled version of {@link #testRemovalNotification_clear} - this is
   * a black-box test that tries to create lots of different thread-interleavings, and asserts that
   * each computation is affected by a call to {@code clear()} (and therefore gets passed to the
   * removal listener), or else is not affected by the {@code clear()} (and therefore exists in the
   * cache afterward).
   */