feat(fs): file writes update the file cache (#6186)

Co-authored-by: kevinkang-Globe <139213362+kevinkang-Globe@users.noreply.github.com>

docs/conf.py

@@ -42,7 +42,8 @@ extensions = [
     'sphinx_sitemap',
     'lv_example',
     'sphinx_rtd_dark_mode',
-    'link_roles'
+    'link_roles',
+    'sphinxcontrib.mermaid'
 ]
 
 default_dark_mode = False

docs/libs/fs.rst

@@ -34,7 +34,7 @@ The work directory can be set with ``LV_FS_..._PATH``. E.g.
 ``"/home/joe/projects/"`` The actual file/directory paths will be
 appended to it.
 
-Cached reading is also supported if ``LV_FS_..._CACHE_SIZE`` is set to
+:ref:`Cached reading <overview_file_system_cache>` is also supported if ``LV_FS_..._CACHE_SIZE`` is set to
 not ``0`` value. :cpp:func:`lv_fs_read` caches this size of data to lower the
 number of actual reads from the storage.
 

docs/overview/fs.rst

@@ -155,6 +155,95 @@ To use files in image widgets the following callbacks are required:
 - seek
 - tell
 
+.. _overview_file_system_cache:
+
+Optional file buffering/caching
+*******************************
+
+Files will buffer their reads if the corresponding ``LV_FS_*_CACHE_SIZE``
+config option is set to a value greater than zero. Each open file will
+buffer up to that many bytes to reduce the number of FS driver calls.
+
+Generally speaking, file buffering can be optimized for different kinds
+of access patterns. The one implemented here is optimal for reading large
+files in chunks, which is what the image decoder does.
+It has the potential to call the driver's ``read`` fewer
+times than ``lv_fs_read`` is called. In the best case where the cache size is
+\>= the size of the file, ``read`` will only be called once. This strategy is good
+for linear reading of large files but less helpful for short random reads across a file bigger than the buffer
+since data will be buffered that will be discarded after the next seek and read.
+The cache should be sufficiently large or disabled in that case. Another case where the cache should be disabled
+is if the file contents are expected to change by an external factor like with special OS files.
+
+The implementation is documented below. Note that the FS functions make calls
+to other driver FS functions when the cache is enabled. i.e., ``lv_fs_read`` may call the driver's ``seek``
+so the driver needs to implement more callbacks when the cache is enabled.
+
+``lv_fs_read`` :sub:`(behavior when the cache is enabled)`
+-------------------------------------------------
+
+.. mermaid::
+   :zoom:
+
+   %%{init: {'theme':'neutral'}}%%
+   flowchart LR
+       A["call lv_fs_read and
+          the cache is enabled"] --> B{{"is there cached data
+                                         at the file position?"}}
+       B -->|yes| C{{"does the cache have
+                      all required bytes available?"}}
+       C -->|yes| D["copy all required bytes from
+                     the cache to the destination
+                     buffer"]
+       C -->|no| F["copy the available
+                    required bytes
+                    until the end of the cache
+                    into the destination buffer"]
+             --> G["seek the real file to the end
+                    of what the cache had available"]
+             --> H{{"is the number of remaining bytes
+                     larger than the size of the whole cache?"}}
+       H -->|yes| I["read the remaining bytes
+                     from the real file to the
+                     destination buffer"]
+       H -->|no| J["eagerly read the real file
+                    to fill the whole cache
+                    or as many bytes as the
+                    read call can"]
+             --> O["copy the required bytes
+                    to the destination buffer"]
+       B -->|no| K["seek the real file to
+                    the file position"]
+             --> L{{"is the number of required
+                     bytes greater than the
+                     size of the entire cache?"}}
+       L -->|yes| M["read the real file to
+                     the destination buffer"]
+       L -->|no| N["eagerly read the real file
+                    to fill the whole cache
+                    or as many bytes as the
+                    read call can"]
+             --> P["copy the required bytes
+                    to the destination buffer"]
+
+``lv_fs_write`` :sub:`(behavior when the cache is enabled)`
+--------------------------------------------------
+
+The part of the cache that coincides with the written content
+will be updated to reflect the written content.
+
+``lv_fs_seek`` :sub:`(behavior when the cache is enabled)`
+-------------------------------------------------
+
+The driver's ``seek`` will not actually be called unless the ``whence``
+is ``LV_FS_SEEK_END``, in which case ``seek`` and ``tell`` will be called
+to determine where the end of the file is.
+
+``lv_fs_tell`` :sub:`(behavior when the cache is enabled)`
+-------------------------------------------------
+
+The driver's ``tell`` will not actually be called.
+
 .. _overview_file_system_api:
 
 API

docs/requirements.txt

@@ -10,5 +10,6 @@ sphinxcontrib-htmlhelp
 sphinxcontrib-jsmath
 sphinxcontrib-qthelp
 sphinxcontrib-serializinghtml
+sphinxcontrib-mermaid
 sphinx-rtd-dark-mode
 typing-extensions

src/misc/lv_fs.c

@@ -27,6 +27,9 @@
  *  STATIC PROTOTYPES
  **********************/
 static const char * lv_fs_get_real_path(const char * path);
+static lv_fs_res_t lv_fs_read_cached(lv_fs_file_t * file_p, void * buf, uint32_t btr, uint32_t * br);
+static lv_fs_res_t lv_fs_write_cached(lv_fs_file_t * file_p, const void * buf, uint32_t btw, uint32_t * bw);
+static lv_fs_res_t lv_fs_seek_cached(lv_fs_file_t * file_p, uint32_t pos, lv_fs_whence_t whence);
 
 /**********************
  *  STATIC VARIABLES
@@ -171,100 +174,17 @@ lv_fs_res_t lv_fs_close(lv_fs_file_t * file_p)
     return res;
 }
 
-static lv_fs_res_t lv_fs_read_cached(lv_fs_file_t * file_p, char * buf, uint32_t btr, uint32_t * br)
-{
-    LV_PROFILER_BEGIN;
-
-    lv_fs_res_t res = LV_FS_RES_OK;
-    uint32_t file_position = file_p->cache->file_position;
-    uint32_t start = file_p->cache->start;
-    uint32_t end = file_p->cache->end;
-    char * buffer = file_p->cache->buffer;
-    uint32_t buffer_size = file_p->drv->cache_size;
-
-    if(start <= file_position && file_position <= end) {
-        /* Data can be read from cache buffer */
-        uint32_t buffer_remaining_length = (uint32_t)end - file_position + 1;
-        uint32_t buffer_offset = (end - start) - buffer_remaining_length + 1;
-
-        /* Do not allow reading beyond the actual memory block for memory-mapped files */
-        if(file_p->drv->cache_size == LV_FS_CACHE_FROM_BUFFER) {
-            if(btr > buffer_remaining_length)
-                btr = buffer_remaining_length - 1;
-        }
-
-        if(btr <= buffer_remaining_length) {
-            /*Data is in cache buffer, and buffer end not reached, no need to read from FS*/
-            lv_memcpy(buf, buffer + buffer_offset, btr);
-            *br = btr;
-        }
-        else {
-            /*First part of data is in cache buffer, but we need to read rest of data from FS*/
-            lv_memcpy(buf, buffer + buffer_offset, buffer_remaining_length);
-
-            file_p->drv->seek_cb(file_p->drv, file_p->file_d, file_p->cache->end + 1,
-                                 LV_FS_SEEK_SET);
-
-            uint32_t bytes_read_to_buffer = 0;
-            if(btr - buffer_remaining_length > buffer_size) {
-                /*If remaining data chuck is bigger than buffer size, then do not use cache, instead read it directly from FS*/
-                res = file_p->drv->read_cb(file_p->drv, file_p->file_d, (void *)(buf + buffer_remaining_length),
-                                           btr - buffer_remaining_length, &bytes_read_to_buffer);
-            }
-            else {
-                /*If remaining data chunk is smaller than buffer size, then read into cache buffer*/
-                res = file_p->drv->read_cb(file_p->drv, file_p->file_d, (void *)buffer, buffer_size, &bytes_read_to_buffer);
-                file_p->cache->start = file_p->cache->end + 1;
-                file_p->cache->end = file_p->cache->start + bytes_read_to_buffer - 1;
-
-                uint16_t data_chunk_remaining = LV_MIN(btr - buffer_remaining_length, bytes_read_to_buffer);
-                lv_memcpy(buf + buffer_remaining_length, buffer, data_chunk_remaining);
-            }
-            *br = LV_MIN(buffer_remaining_length + bytes_read_to_buffer, btr);
-        }
-    }
-    else {
-        file_p->drv->seek_cb(file_p->drv, file_p->file_d, file_p->cache->file_position,
-                             LV_FS_SEEK_SET);
-
-        /*Data is not in cache buffer*/
-        if(btr > buffer_size) {
-            /*If bigger data is requested, then do not use cache, instead read it directly*/
-            res = file_p->drv->read_cb(file_p->drv, file_p->file_d, (void *)buf, btr, br);
-        }
-        else {
-            /*If small data is requested, then read from FS into cache buffer*/
-            if(buffer == NULL) {
-                file_p->cache->buffer = lv_malloc(buffer_size);
-                LV_ASSERT_MALLOC(file_p->cache->buffer);
-                buffer = file_p->cache->buffer;
-            }
-
-            uint32_t bytes_read_to_buffer = 0;
-            res = file_p->drv->read_cb(file_p->drv, file_p->file_d, (void *)buffer, buffer_size, &bytes_read_to_buffer);
-            file_p->cache->start = file_position;
-            file_p->cache->end = file_p->cache->start + bytes_read_to_buffer - 1;
-
-            *br = LV_MIN(btr, bytes_read_to_buffer);
-            lv_memcpy(buf, buffer, *br);
-
-        }
-    }
-
-    if(res == LV_FS_RES_OK) {
-        file_p->cache->file_position += *br;
-    }
-
-    LV_PROFILER_END;
-
-    return res;
-}
-
 lv_fs_res_t lv_fs_read(lv_fs_file_t * file_p, void * buf, uint32_t btr, uint32_t * br)
 {
     if(br != NULL) *br = 0;
     if(file_p->drv == NULL) return LV_FS_RES_INV_PARAM;
-    if(file_p->drv->read_cb == NULL) return LV_FS_RES_NOT_IMP;
+
+    if(file_p->drv->cache_size) {
+        if(file_p->drv->read_cb == NULL || file_p->drv->seek_cb == NULL) return LV_FS_RES_NOT_IMP;
+    }
+    else {
+        if(file_p->drv->read_cb == NULL) return LV_FS_RES_NOT_IMP;
+    }
 
     LV_PROFILER_BEGIN;
 
@@ -272,7 +192,7 @@ lv_fs_res_t lv_fs_read(lv_fs_file_t * file_p, void * buf, uint32_t btr, uint32_t
     lv_fs_res_t res;
 
     if(file_p->drv->cache_size) {
-        res = lv_fs_read_cached(file_p, (char *)buf, btr, &br_tmp);
+        res = lv_fs_read_cached(file_p, buf, btr, &br_tmp);
     }
     else {
         res = file_p->drv->read_cb(file_p->drv, file_p->file_d, buf, btr, &br_tmp);
@@ -293,30 +213,25 @@ lv_fs_res_t lv_fs_write(lv_fs_file_t * file_p, const void * buf, uint32_t btw, u
         return LV_FS_RES_INV_PARAM;
     }
 
-    if(file_p->drv->write_cb == NULL) {
+    if(file_p->drv->cache_size) {
-        return LV_FS_RES_NOT_IMP;
+        if(file_p->drv->write_cb == NULL || file_p->drv->seek_cb == NULL) return LV_FS_RES_NOT_IMP;
+    }
+    else {
+        if(file_p->drv->write_cb == NULL) return LV_FS_RES_NOT_IMP;
     }
 
     LV_PROFILER_BEGIN;
 
-    lv_fs_res_t res = LV_FS_RES_OK;
+    lv_fs_res_t res;
-
-    /*Need to do FS seek before writing data to FS*/
-    if(file_p->drv->cache_size) {
-        res = file_p->drv->seek_cb(file_p->drv, file_p->file_d, file_p->cache->file_position, LV_FS_SEEK_SET);
-        if(res != LV_FS_RES_OK) {
-            LV_PROFILER_END;
-            return res;
-        }
-    }
-
     uint32_t bw_tmp = 0;
-    res = file_p->drv->write_cb(file_p->drv, file_p->file_d, buf, btw, &bw_tmp);
+    if(file_p->drv->cache_size) {
+        res = lv_fs_write_cached(file_p, buf, btw, &bw_tmp);
+    }
+    else {
+        res = file_p->drv->write_cb(file_p->drv, file_p->file_d, buf, btw, &bw_tmp);
+    }
     if(bw != NULL) *bw = bw_tmp;
 
-    if(file_p->drv->cache_size && res == LV_FS_RES_OK)
-        file_p->cache->file_position += bw_tmp;
-
     LV_PROFILER_END;
 
     return res;
@@ -328,49 +243,18 @@ lv_fs_res_t lv_fs_seek(lv_fs_file_t * file_p, uint32_t pos, lv_fs_whence_t whenc
         return LV_FS_RES_INV_PARAM;
     }
 
-    if(file_p->drv->seek_cb == NULL) {
+    if(file_p->drv->cache_size) {
-        return LV_FS_RES_NOT_IMP;
+        if(file_p->drv->seek_cb == NULL || file_p->drv->tell_cb == NULL) return LV_FS_RES_NOT_IMP;
+    }
+    else {
+        if(file_p->drv->seek_cb == NULL) return LV_FS_RES_NOT_IMP;
     }
 
     LV_PROFILER_BEGIN;
 
-    lv_fs_res_t res = LV_FS_RES_OK;
+    lv_fs_res_t res;
     if(file_p->drv->cache_size) {
-        switch(whence) {
+        res = lv_fs_seek_cached(file_p, pos, whence);
-            case LV_FS_SEEK_SET: {
-                    file_p->cache->file_position = pos;
-
-                    /*FS seek if new position is outside cache buffer*/
-                    if(file_p->cache->file_position < file_p->cache->start || file_p->cache->file_position > file_p->cache->end) {
-                        res = file_p->drv->seek_cb(file_p->drv, file_p->file_d, file_p->cache->file_position, LV_FS_SEEK_SET);
-                    }
-
-                    break;
-                }
-            case LV_FS_SEEK_CUR: {
-                    file_p->cache->file_position += pos;
-
-                    /*FS seek if new position is outside cache buffer*/
-                    if(file_p->cache->file_position < file_p->cache->start || file_p->cache->file_position > file_p->cache->end) {
-                        res = file_p->drv->seek_cb(file_p->drv, file_p->file_d, file_p->cache->file_position, LV_FS_SEEK_SET);
-                    }
-
-                    break;
-                }
-            case LV_FS_SEEK_END: {
-                    /*Because we don't know the file size, we do a little trick: do a FS seek, then get the new file position from FS*/
-                    res = file_p->drv->seek_cb(file_p->drv, file_p->file_d, pos, whence);
-                    if(res == LV_FS_RES_OK) {
-                        uint32_t tmp_position;
-                        res = file_p->drv->tell_cb(file_p->drv, file_p->file_d, &tmp_position);
-
-                        if(res == LV_FS_RES_OK) {
-                            file_p->cache->file_position = tmp_position;
-                        }
-                    }
-                    break;
-                }
-        }
     }
     else {
         res = file_p->drv->seek_cb(file_p->drv, file_p->file_d, pos, whence);
@@ -388,7 +272,7 @@ lv_fs_res_t lv_fs_tell(lv_fs_file_t * file_p, uint32_t * pos)
         return LV_FS_RES_INV_PARAM;
     }
 
-    if(file_p->drv->tell_cb == NULL) {
+    if(file_p->drv->cache_size == 0 && file_p->drv->tell_cb == NULL) {
         *pos = 0;
         return LV_FS_RES_NOT_IMP;
     }
@@ -621,3 +505,162 @@ static const char * lv_fs_get_real_path(const char * path)
 
     return path;
 }
+
+static lv_fs_res_t lv_fs_read_cached(lv_fs_file_t * file_p, void * buf, uint32_t btr, uint32_t * br)
+{
+    lv_fs_res_t res = LV_FS_RES_OK;
+    uint32_t file_position = file_p->cache->file_position;
+    uint32_t start = file_p->cache->start;
+    uint32_t end = file_p->cache->end;
+    char * buffer = file_p->cache->buffer;
+    uint32_t buffer_size = file_p->drv->cache_size;
+
+    if(start <= file_position && file_position <= end) {
+        /* Data can be read from cache buffer */
+        uint32_t buffer_remaining_length = (uint32_t)end - file_position + 1;
+        uint32_t buffer_offset = (end - start) - buffer_remaining_length + 1;
+
+        /* Do not allow reading beyond the actual memory block for memory-mapped files */
+        if(file_p->drv->cache_size == LV_FS_CACHE_FROM_BUFFER) {
+            if(btr > buffer_remaining_length)
+                btr = buffer_remaining_length - 1;
+        }
+
+        if(btr <= buffer_remaining_length) {
+            /*Data is in cache buffer, and buffer end not reached, no need to read from FS*/
+            lv_memcpy(buf, buffer + buffer_offset, btr);
+            *br = btr;
+        }
+        else {
+            /*First part of data is in cache buffer, but we need to read rest of data from FS*/
+            lv_memcpy(buf, buffer + buffer_offset, buffer_remaining_length);
+
+            file_p->drv->seek_cb(file_p->drv, file_p->file_d, file_p->cache->end + 1,
+                                 LV_FS_SEEK_SET);
+
+            uint32_t bytes_read_to_buffer = 0;
+            if(btr - buffer_remaining_length > buffer_size) {
+                /*If remaining data chuck is bigger than buffer size, then do not use cache, instead read it directly from FS*/
+                res = file_p->drv->read_cb(file_p->drv, file_p->file_d, (char *)buf + buffer_remaining_length,
+                                           btr - buffer_remaining_length, &bytes_read_to_buffer);
+            }
+            else {
+                /*If remaining data chunk is smaller than buffer size, then read into cache buffer*/
+                res = file_p->drv->read_cb(file_p->drv, file_p->file_d, buffer, buffer_size, &bytes_read_to_buffer);
+                file_p->cache->start = file_p->cache->end + 1;
+                file_p->cache->end = file_p->cache->start + bytes_read_to_buffer - 1;
+
+                uint16_t data_chunk_remaining = LV_MIN(btr - buffer_remaining_length, bytes_read_to_buffer);
+                lv_memcpy((char *)buf + buffer_remaining_length, buffer, data_chunk_remaining);
+            }
+            *br = LV_MIN(buffer_remaining_length + bytes_read_to_buffer, btr);
+        }
+    }
+    else {
+        file_p->drv->seek_cb(file_p->drv, file_p->file_d, file_p->cache->file_position,
+                             LV_FS_SEEK_SET);
+
+        /*Data is not in cache buffer*/
+        if(btr > buffer_size) {
+            /*If bigger data is requested, then do not use cache, instead read it directly*/
+            res = file_p->drv->read_cb(file_p->drv, file_p->file_d, (void *)buf, btr, br);
+        }
+        else {
+            /*If small data is requested, then read from FS into cache buffer*/
+            if(buffer == NULL) {
+                file_p->cache->buffer = lv_malloc(buffer_size);
+                LV_ASSERT_MALLOC(file_p->cache->buffer);
+                buffer = file_p->cache->buffer;
+            }
+
+            uint32_t bytes_read_to_buffer = 0;
+            res = file_p->drv->read_cb(file_p->drv, file_p->file_d, (void *)buffer, buffer_size, &bytes_read_to_buffer);
+            file_p->cache->start = file_position;
+            file_p->cache->end = file_p->cache->start + bytes_read_to_buffer - 1;
+
+            *br = LV_MIN(btr, bytes_read_to_buffer);
+            lv_memcpy(buf, buffer, *br);
+
+        }
+    }
+
+    if(res == LV_FS_RES_OK) {
+        file_p->cache->file_position += *br;
+    }
+
+    return res;
+}
+
+static lv_fs_res_t lv_fs_write_cached(lv_fs_file_t * file_p, const void * buf, uint32_t btw, uint32_t * bw)
+{
+    lv_fs_res_t res = LV_FS_RES_OK;
+
+    /*Need to do FS seek before writing data to FS*/
+    res = file_p->drv->seek_cb(file_p->drv, file_p->file_d, file_p->cache->file_position, LV_FS_SEEK_SET);
+    if(res != LV_FS_RES_OK) return res;
+
+    res = file_p->drv->write_cb(file_p->drv, file_p->file_d, buf, btw, bw);
+    if(res != LV_FS_RES_OK) return res;
+
+    if(file_p->cache->end >= file_p->cache->start) {
+        uint32_t start_position = file_p->cache->file_position;
+        uint32_t end_position = file_p->cache->file_position + *bw - 1;
+        char * cache_buffer = file_p->cache->buffer;
+        const char * write_buffer = buf;
+
+        if(start_position <= file_p->cache->start && end_position >= file_p->cache->end) {
+            lv_memcpy(cache_buffer,
+                      write_buffer + (file_p->cache->start - start_position),
+                      file_p->cache->end + 1 - file_p->cache->start);
+        }
+        else if(start_position >= file_p->cache->start && end_position <= file_p->cache->end) {
+            lv_memcpy(cache_buffer + (start_position - file_p->cache->start),
+                      write_buffer,
+                      end_position + 1 - start_position);
+        }
+        else if(end_position >= file_p->cache->start && end_position <= file_p->cache->end) {
+            lv_memcpy(cache_buffer,
+                      write_buffer + (file_p->cache->start - start_position),
+                      end_position + 1 - file_p->cache->start);
+        }
+        else if(start_position >= file_p->cache->start && start_position <= file_p->cache->end) {
+            lv_memcpy(cache_buffer + (start_position - file_p->cache->start),
+                      write_buffer,
+                      file_p->cache->end + 1 - start_position);
+        }
+    }
+
+    file_p->cache->file_position += *bw;
+
+    return res;
+}
+
+static lv_fs_res_t lv_fs_seek_cached(lv_fs_file_t * file_p, uint32_t pos, lv_fs_whence_t whence)
+{
+    lv_fs_res_t res = LV_FS_RES_OK;
+    switch(whence) {
+        case LV_FS_SEEK_SET: {
+                file_p->cache->file_position = pos;
+                break;
+            }
+        case LV_FS_SEEK_CUR: {
+                file_p->cache->file_position += pos;
+                break;
+            }
+        case LV_FS_SEEK_END: {
+                /*Because we don't know the file size, we do a little trick: do a FS seek, then get the new file position from FS*/
+                res = file_p->drv->seek_cb(file_p->drv, file_p->file_d, pos, whence);
+                if(res == LV_FS_RES_OK) {
+                    uint32_t tmp_position;
+                    res = file_p->drv->tell_cb(file_p->drv, file_p->file_d, &tmp_position);
+
+                    if(res == LV_FS_RES_OK) {
+                        file_p->cache->file_position = tmp_position;
+                    }
+                }
+                break;
+            }
+    }
+
+    return res;
+}

tests/src/test_cases/test_fs.c

@@ -178,4 +178,99 @@ static void read_random_drv(char drv_letter, uint32_t cache_size)
     drv->cache_size = original_cache_size;
 }
 
+void test_write_read_random(void)
+{
+    lv_fs_drv_t * drv = lv_fs_get_drv('A');
+    uint32_t original_cache_size = drv->cache_size;
+    drv->cache_size = 7;
+
+    /* create the file and reopen for read+write. stdio "rb+" mode requires the file to exist */
+    lv_fs_res_t res;
+    lv_fs_file_t f;
+    res = lv_fs_open(&f, "A:fs_write_read_random.bin", LV_FS_MODE_WR);
+    TEST_ASSERT_EQUAL(LV_FS_RES_OK, res);
+    res = lv_fs_close(&f);
+    TEST_ASSERT_EQUAL(LV_FS_RES_OK, res);
+    res = lv_fs_open(&f, "A:fs_write_read_random.bin", LV_FS_MODE_WR | LV_FS_MODE_RD);
+    TEST_ASSERT_EQUAL(LV_FS_RES_OK, res);
+
+    uint8_t buf1000[1000];
+    for(uint32_t i = 0; i < 1000; i++) buf1000[i] = i;
+    res = lv_fs_write(&f, buf1000, 1000, NULL);
+    TEST_ASSERT_EQUAL(LV_FS_RES_OK, res);
+
+    /**
+     * {{{action, amount}, ... x20 actions per combo}, ... x100 combos}
+     * actions are read (0), write (1), seek (2)
+     * read and write amount ranges from 1 to 20. seek amount ranges from -20 to 20.
+     * seeks occur as frequently as reads+writes combined.
+     */
+    // *INDENT-OFF*
+    static const int8_t actions[100][20][2] = {
+        {{2, -20}, {2, 17}, {0, 20}, {2, 19}, {1, 18}, {1, 4}, {1, 13}, {2, -7}, {1, 6}, {1, 19}, {2, 3}, {1, 12}, {2, 12}, {2, -2}, {2, -20}, {2, -17}, {1, 15}, {2, -17}, {0, 18}, {2, 14}}, {{2, 19}, {2, 17}, {2, -12}, {2, -5}, {2, -1}, {2, -17}, {1, 4}, {2, 19}, {2, 3}, {2, 1}, {2, 10}, {2, 18}, {0, 10}, {2, 8}, {2, 17}, {2, 20}, {0, 5}, {0, 14}, {0, 6}, {1, 8}}, {{0, 1}, {2, -20}, {2, -12}, {1, 9}, {0, 9}, {2, 19}, {1, 8}, {0, 13}, {0, 5}, {2, -7}, {2, -14}, {0, 8}, {2, 13}, {1, 5}, {0, 3}, {0, 16}, {2, 19}, {0, 4}, {1, 6}, {2, -4}}, {{0, 1}, {2, 12}, {1, 7}, {1, 17}, {1, 19}, {0, 8}, {1, 1}, {2, 9}, {2, -14}, {2, 14}, {2, -17}, {2, 11}, {1, 4}, {2, 19}, {2, -18}, {1, 12}, {2, -14}, {0, 9}, {1, 7}, {2, 17}}, {{2, -6}, {0, 13}, {1, 15}, {1, 8}, {2, -1}, {2, 15}, {2, 3}, {2, -16}, {2, -11}, {2, 14}, {2, -19}, {2, 6}, {1, 10}, {1, 6}, {1, 12}, {2, 12}, {0, 10}, {2, 10}, {2, -4}, {2, 5}}, {{2, -6}, {1, 2}, {1, 11}, {1, 19}, {2, 2}, {2, 20}, {2, -19}, {2, -7}, {0, 13}, {2, 4}, {1, 6}, {0, 9}, {0, 6}, {2, -1}, {2, -5}, {2, 14}, {2, 15}, {0, 4}, {0, 6}, {0, 10}}, {{1, 17}, {1, 17}, {0, 15}, {0, 3}, {1, 8}, {2, -9}, {1, 13}, {0, 20}, {0, 3}, {1, 17}, {2, -8}, {2, -1}, {1, 13}, {0, 13}, {0, 8}, {1, 1}, {2, -4}, {2, 13}, {2, 17}, {2, -14}}, {{1, 17}, {1, 13}, {1, 17}, {1, 5}, {1, 3}, {0, 20}, {2, 12}, {0, 13}, {2, 5}, {2, -10}, {2, 10}, {0, 6}, {2, 18}, {0, 17}, {2, 2}, {1, 5}, {2, 16}, {2, -10}, {0, 2}, {2, -9}}, {{2, 7}, {2, -2}, {1, 14}, {0, 15}, {1, 2}, {2, 6}, {2, 11}, {1, 2}, {0, 12}, {2, 9}, {0, 17}, {0, 15}, {2, -19}, {0, 11}, {2, 3}, {2, 15}, {2, 19}, {2, -16}, {1, 6}, {1, 15}}, {{2, 12}, {1, 2}, {2, -4}, {2, -20}, {0, 18}, {2, -16}, {1, 15}, {2, -9}, {2, -7}, {1, 1}, {0, 7}, {0, 18}, {1, 18}, {0, 2}, {2, 17}, {1, 2}, {1, 8}, {1, 18}, {2, -7}, {0, 2}},
+        {{2, 19}, {2, 17}, {2, -7}, {0, 17}, {0, 18}, {1, 4}, {1, 1}, {0, 3}, {2, 4}, {2, -4}, {1, 20}, {0, 1}, {2, 20}, {0, 6}, {2, 10}, {0, 19}, {2, -1}, {0, 7}, {0, 16}, {1, 13}}, {{2, 10}, {2, 13}, {2, 15}, {2, 3}, {2, 12}, {0, 14}, {2, 6}, {2, 14}, {2, -13}, {2, 18}, {0, 19}, {2, -8}, {2, -9}, {0, 12}, {2, -20}, {2, -6}, {2, 15}, {2, 18}, {1, 18}, {1, 10}}, {{0, 15}, {2, -6}, {2, 17}, {1, 7}, {0, 9}, {0, 11}, {0, 12}, {0, 20}, {2, -1}, {2, -8}, {0, 13}, {2, 19}, {1, 3}, {0, 18}, {1, 13}, {2, 12}, {2, 13}, {1, 5}, {2, -14}, {2, 18}}, {{0, 6}, {1, 4}, {1, 6}, {0, 2}, {2, 8}, {1, 9}, {2, 20}, {0, 9}, {2, -1}, {2, 5}, {0, 18}, {2, 8}, {2, 12}, {2, -14}, {0, 18}, {1, 1}, {2, -15}, {2, 14}, {2, -11}, {2, -2}}, {{1, 4}, {2, 6}, {2, 18}, {1, 19}, {0, 18}, {0, 19}, {0, 14}, {0, 12}, {2, 3}, {0, 19}, {2, -20}, {0, 8}, {2, -15}, {2, -15}, {0, 8}, {1, 17}, {2, 2}, {1, 14}, {0, 11}, {0, 13}}, {{2, -10}, {2, -8}, {1, 18}, {1, 11}, {1, 5}, {0, 2}, {2, -19}, {2, -9}, {1, 5}, {2, -1}, {2, 2}, {1, 5}, {0, 9}, {0, 17}, {2, 2}, {0, 10}, {1, 12}, {1, 10}, {0, 8}, {2, -13}}, {{0, 13}, {1, 5}, {2, -1}, {2, -16}, {2, 2}, {0, 6}, {2, -11}, {0, 5}, {2, 5}, {2, -6}, {2, -6}, {1, 19}, {0, 8}, {2, -16}, {2, 14}, {0, 11}, {0, 14}, {0, 18}, {0, 14}, {2, 1}}, {{2, 3}, {2, -2}, {0, 10}, {1, 1}, {0, 10}, {2, -15}, {2, 19}, {2, 2}, {1, 15}, {1, 10}, {2, -18}, {0, 20}, {0, 10}, {2, 3}, {1, 13}, {0, 8}, {0, 16}, {0, 14}, {2, 13}, {2, -7}}, {{0, 4}, {1, 7}, {0, 2}, {0, 15}, {0, 20}, {1, 9}, {0, 14}, {2, 18}, {0, 1}, {0, 4}, {2, -17}, {1, 10}, {1, 15}, {0, 2}, {2, -6}, {2, 4}, {2, 4}, {2, 17}, {2, -13}, {1, 20}}, {{1, 8}, {0, 20}, {2, 4}, {1, 6}, {2, -19}, {1, 4}, {0, 5}, {1, 8}, {1, 17}, {2, -4}, {2, 14}, {1, 10}, {2, 7}, {1, 18}, {2, 17}, {1, 6}, {0, 20}, {2, 1}, {2, -12}, {2, 18}},
+        {{2, -7}, {1, 12}, {2, 4}, {2, 14}, {0, 13}, {1, 17}, {2, -2}, {2, -9}, {2, -13}, {1, 4}, {2, 4}, {1, 5}, {0, 15}, {2, -11}, {2, 3}, {2, 1}, {2, -11}, {2, 11}, {2, -11}, {0, 4}}, {{1, 7}, {2, 20}, {0, 6}, {0, 9}, {1, 2}, {0, 11}, {2, 4}, {2, -19}, {0, 17}, {2, -7}, {0, 20}, {0, 10}, {1, 11}, {1, 20}, {1, 6}, {2, 14}, {0, 11}, {0, 19}, {2, 4}, {1, 8}}, {{0, 9}, {2, -3}, {1, 17}, {2, 14}, {2, 3}, {1, 19}, {2, 17}, {0, 18}, {2, 16}, {0, 9}, {2, -15}, {1, 14}, {2, 11}, {2, -7}, {0, 17}, {2, 12}, {2, 6}, {2, 9}, {0, 7}, {1, 3}}, {{0, 1}, {2, 13}, {1, 19}, {0, 19}, {2, 6}, {2, -14}, {2, 8}, {2, -18}, {2, 4}, {2, -7}, {0, 12}, {2, 15}, {1, 3}, {2, -19}, {2, 15}, {2, -2}, {1, 19}, {1, 18}, {1, 19}, {0, 16}}, {{2, 7}, {2, 14}, {2, 14}, {2, -19}, {0, 1}, {2, -5}, {0, 17}, {2, 2}, {2, 15}, {1, 13}, {0, 20}, {0, 12}, {2, 20}, {0, 9}, {2, -8}, {0, 14}, {1, 19}, {2, -15}, {2, 17}, {2, -12}}, {{0, 16}, {2, -7}, {2, -4}, {1, 11}, {1, 17}, {2, -14}, {0, 16}, {2, 6}, {1, 19}, {2, 17}, {2, 10}, {2, -12}, {2, -17}, {1, 4}, {2, -14}, {2, -7}, {2, -17}, {2, -1}, {2, -16}, {1, 8}}, {{0, 5}, {0, 15}, {2, 4}, {2, 20}, {2, 7}, {2, 3}, {2, 17}, {0, 8}, {0, 18}, {2, -18}, {1, 1}, {0, 15}, {2, -4}, {0, 13}, {1, 11}, {0, 4}, {2, 11}, {1, 11}, {1, 10}, {2, -9}}, {{2, -5}, {2, -16}, {1, 2}, {1, 17}, {2, 9}, {2, -2}, {0, 7}, {0, 14}, {2, -10}, {0, 6}, {1, 14}, {1, 15}, {2, 12}, {2, 11}, {2, -9}, {2, -10}, {2, -14}, {2, 9}, {0, 13}, {2, 5}}, {{2, 8}, {2, -16}, {2, 20}, {1, 8}, {1, 2}, {2, -5}, {2, -20}, {1, 2}, {1, 4}, {1, 9}, {0, 19}, {2, -18}, {0, 6}, {0, 13}, {1, 5}, {2, 2}, {0, 4}, {1, 19}, {2, 15}, {1, 12}}, {{2, -8}, {0, 16}, {1, 10}, {2, 5}, {2, -16}, {0, 3}, {2, 5}, {0, 6}, {1, 17}, {2, 1}, {2, 13}, {0, 3}, {0, 6}, {0, 6}, {0, 19}, {1, 13}, {2, 19}, {2, 5}, {1, 16}, {2, 5}},
+        {{2, -19}, {2, -1}, {0, 19}, {2, -3}, {2, 13}, {2, -12}, {0, 2}, {2, -20}, {2, 15}, {2, -9}, {2, -2}, {2, 13}, {2, -6}, {0, 2}, {1, 6}, {2, -1}, {0, 12}, {0, 20}, {2, -14}, {1, 2}}, {{1, 9}, {2, -14}, {2, -2}, {2, -13}, {0, 3}, {1, 6}, {2, 20}, {2, 11}, {2, 17}, {2, 5}, {0, 5}, {1, 1}, {2, -9}, {1, 8}, {2, -2}, {0, 18}, {2, -8}, {1, 11}, {2, 6}, {1, 7}}, {{2, 17}, {2, 14}, {2, 16}, {1, 20}, {2, -1}, {2, -7}, {1, 3}, {1, 14}, {0, 1}, {0, 18}, {2, -14}, {0, 10}, {0, 18}, {2, 19}, {1, 13}, {2, -16}, {1, 17}, {1, 1}, {2, -13}, {0, 13}}, {{2, -2}, {0, 14}, {0, 12}, {2, -8}, {1, 16}, {0, 18}, {2, 5}, {2, 13}, {1, 14}, {2, -4}, {2, 16}, {2, -16}, {2, 16}, {1, 18}, {2, 15}, {2, 4}, {2, -5}, {1, 7}, {2, -20}, {2, -9}}, {{2, 18}, {2, 2}, {2, 5}, {0, 4}, {2, 17}, {2, -15}, {2, 8}, {2, -11}, {1, 8}, {2, -6}, {2, -13}, {0, 5}, {0, 18}, {0, 15}, {2, -8}, {2, -15}, {1, 1}, {2, 4}, {2, -9}, {2, 14}}, {{2, -1}, {2, 1}, {1, 12}, {0, 9}, {2, -11}, {1, 4}, {1, 11}, {1, 5}, {0, 12}, {2, -7}, {1, 1}, {0, 6}, {0, 15}, {2, -10}, {2, -18}, {2, -12}, {0, 3}, {2, 2}, {2, -17}, {2, 1}}, {{2, -5}, {2, 18}, {1, 2}, {2, 14}, {2, 20}, {0, 13}, {0, 11}, {0, 6}, {2, -7}, {2, 13}, {1, 13}, {2, -1}, {1, 12}, {2, -9}, {2, 3}, {1, 6}, {2, -16}, {0, 6}, {0, 9}, {2, -14}}, {{1, 6}, {2, 7}, {2, -13}, {0, 5}, {1, 4}, {0, 15}, {2, 18}, {2, -4}, {2, 16}, {1, 1}, {2, 17}, {0, 2}, {1, 12}, {0, 17}, {1, 18}, {1, 5}, {1, 8}, {1, 4}, {2, -9}, {1, 9}}, {{0, 20}, {1, 10}, {2, 20}, {2, 13}, {0, 18}, {0, 10}, {1, 3}, {0, 8}, {2, -16}, {2, -16}, {2, -2}, {0, 20}, {2, -19}, {2, -11}, {1, 17}, {1, 18}, {1, 5}, {0, 6}, {2, -9}, {1, 8}}, {{0, 18}, {0, 19}, {2, 16}, {2, -14}, {1, 7}, {1, 9}, {0, 16}, {0, 16}, {1, 17}, {0, 14}, {2, -16}, {1, 6}, {1, 11}, {2, 7}, {1, 19}, {1, 11}, {2, -14}, {0, 7}, {1, 12}, {0, 2}},
+        {{2, 3}, {2, -15}, {0, 13}, {2, -3}, {0, 16}, {1, 18}, {0, 11}, {0, 16}, {1, 13}, {2, -18}, {1, 14}, {2, 11}, {0, 11}, {2, -14}, {2, -19}, {0, 2}, {2, -7}, {0, 5}, {0, 20}, {2, -7}}, {{2, 9}, {2, 5}, {2, 7}, {0, 15}, {2, 4}, {0, 5}, {2, -17}, {2, 16}, {2, 8}, {0, 11}, {0, 1}, {1, 8}, {2, -5}, {1, 1}, {2, 4}, {2, -4}, {2, -17}, {0, 5}, {1, 10}, {0, 5}}, {{0, 11}, {1, 16}, {1, 18}, {0, 5}, {2, -13}, {0, 5}, {1, 13}, {1, 10}, {1, 11}, {0, 5}, {1, 9}, {1, 4}, {1, 19}, {2, 1}, {1, 19}, {1, 18}, {1, 8}, {2, 2}, {2, -5}, {1, 4}}, {{0, 12}, {1, 16}, {2, -1}, {1, 10}, {1, 10}, {2, -19}, {2, -20}, {1, 17}, {1, 19}, {1, 4}, {2, 12}, {0, 1}, {2, -15}, {2, -1}, {2, -10}, {2, -19}, {0, 18}, {0, 6}, {2, 18}, {0, 18}}, {{1, 10}, {0, 13}, {2, 3}, {0, 20}, {0, 19}, {0, 5}, {0, 9}, {0, 5}, {0, 20}, {0, 9}, {2, 16}, {1, 11}, {0, 12}, {2, -17}, {0, 20}, {0, 14}, {1, 17}, {2, 15}, {1, 7}, {2, -1}}, {{2, -10}, {2, 1}, {0, 2}, {2, -11}, {2, -17}, {2, -10}, {1, 9}, {2, -6}, {2, -19}, {1, 14}, {0, 4}, {1, 6}, {2, -9}, {2, 3}, {1, 2}, {2, 19}, {1, 15}, {0, 7}, {0, 4}, {2, 2}}, {{1, 12}, {2, -8}, {2, 13}, {2, -19}, {0, 17}, {0, 20}, {1, 3}, {1, 15}, {1, 20}, {2, 17}, {0, 12}, {2, -2}, {1, 8}, {2, -12}, {0, 11}, {2, 17}, {1, 14}, {1, 13}, {2, 2}, {2, 3}}, {{0, 13}, {1, 13}, {2, -4}, {1, 17}, {1, 1}, {1, 5}, {0, 10}, {1, 12}, {0, 9}, {2, -16}, {0, 13}, {2, 19}, {2, 9}, {1, 18}, {2, -1}, {2, -14}, {0, 5}, {1, 2}, {0, 20}, {2, -19}}, {{1, 7}, {2, 19}, {2, 11}, {2, -16}, {1, 19}, {2, -14}, {0, 7}, {1, 10}, {2, 8}, {0, 12}, {1, 12}, {2, -11}, {2, 6}, {2, -16}, {2, 15}, {1, 20}, {2, -12}, {1, 7}, {2, -16}, {2, 7}}, {{0, 8}, {2, 19}, {1, 12}, {2, -12}, {2, 4}, {1, 10}, {1, 13}, {2, 2}, {2, -14}, {2, -10}, {2, 18}, {1, 16}, {0, 10}, {2, 19}, {2, -1}, {1, 17}, {2, -1}, {0, 14}, {1, 11}, {0, 18}},
+        {{2, 2}, {2, -2}, {2, 12}, {0, 7}, {0, 14}, {2, -15}, {2, 13}, {2, -3}, {0, 1}, {2, -2}, {1, 2}, {2, 4}, {2, 4}, {2, 16}, {1, 4}, {2, 1}, {1, 9}, {1, 6}, {1, 12}, {1, 11}}, {{2, -10}, {1, 16}, {1, 12}, {0, 18}, {2, -13}, {0, 19}, {2, 15}, {0, 11}, {0, 2}, {0, 4}, {0, 7}, {0, 10}, {2, -10}, {2, 11}, {0, 13}, {0, 10}, {2, -14}, {2, -18}, {0, 7}, {2, 16}}, {{2, -19}, {2, -5}, {1, 9}, {0, 15}, {2, 4}, {2, -14}, {1, 13}, {2, 10}, {2, -7}, {2, 14}, {2, 8}, {2, 9}, {0, 14}, {2, -4}, {1, 2}, {1, 19}, {0, 18}, {2, 18}, {1, 6}, {2, -6}}, {{2, -15}, {2, 1}, {0, 8}, {1, 5}, {2, -11}, {2, -3}, {0, 19}, {0, 4}, {1, 19}, {1, 2}, {1, 2}, {0, 3}, {0, 16}, {2, -3}, {2, 18}, {1, 20}, {2, -16}, {2, -2}, {2, -17}, {1, 15}}, {{1, 19}, {2, -11}, {1, 13}, {0, 14}, {1, 18}, {2, 11}, {2, 13}, {2, -14}, {1, 5}, {2, -6}, {0, 4}, {2, 19}, {0, 12}, {1, 4}, {2, -6}, {2, 8}, {2, 9}, {2, -10}, {2, -3}, {2, -19}}, {{2, 7}, {2, -9}, {2, 5}, {2, 12}, {2, -20}, {2, -3}, {2, -12}, {2, 5}, {0, 6}, {2, 15}, {1, 8}, {1, 9}, {2, 18}, {2, -14}, {2, 10}, {1, 5}, {1, 2}, {0, 14}, {2, 14}, {0, 19}}, {{2, 12}, {0, 9}, {0, 14}, {1, 4}, {2, 4}, {2, -8}, {2, 4}, {0, 13}, {1, 10}, {2, 18}, {2, 13}, {2, 15}, {1, 18}, {2, 7}, {2, -18}, {2, 18}, {1, 9}, {2, -9}, {0, 16}, {2, -14}}, {{0, 16}, {2, 9}, {2, 7}, {1, 6}, {0, 14}, {2, -18}, {1, 14}, {1, 2}, {0, 10}, {1, 6}, {0, 10}, {2, 2}, {1, 1}, {0, 19}, {1, 6}, {2, -3}, {2, 3}, {2, 12}, {2, 5}, {1, 18}}, {{2, -17}, {0, 17}, {0, 5}, {2, 18}, {2, 8}, {0, 14}, {0, 10}, {1, 20}, {2, 7}, {1, 10}, {1, 14}, {1, 10}, {0, 11}, {1, 15}, {0, 16}, {1, 14}, {0, 3}, {2, 16}, {2, -5}, {2, -4}}, {{1, 15}, {2, -9}, {0, 11}, {0, 16}, {2, 1}, {0, 12}, {0, 7}, {0, 16}, {2, 14}, {0, 3}, {1, 11}, {2, 4}, {1, 6}, {2, -1}, {1, 20}, {1, 13}, {0, 2}, {2, -12}, {0, 9}, {2, 8}},
+        {{0, 1}, {2, -4}, {0, 19}, {2, -15}, {2, -16}, {2, -10}, {2, 7}, {0, 10}, {2, -6}, {2, -8}, {2, -3}, {2, 18}, {1, 20}, {2, 10}, {1, 18}, {2, -3}, {0, 7}, {2, 3}, {2, 14}, {2, 15}}, {{1, 17}, {0, 7}, {1, 17}, {2, -8}, {2, -12}, {2, -9}, {2, 15}, {0, 10}, {1, 10}, {2, -6}, {2, -20}, {1, 17}, {2, -9}, {1, 15}, {1, 3}, {1, 8}, {0, 1}, {1, 13}, {2, -5}, {0, 14}}, {{2, 8}, {0, 11}, {0, 12}, {2, 5}, {2, -4}, {2, -5}, {2, -2}, {0, 20}, {2, -4}, {1, 1}, {1, 2}, {0, 4}, {2, 14}, {1, 17}, {2, -13}, {1, 13}, {2, 12}, {2, 20}, {2, 14}, {2, -9}}, {{2, -20}, {2, 13}, {1, 20}, {2, 20}, {2, 9}, {0, 16}, {2, 1}, {0, 13}, {2, 17}, {2, 8}, {2, 13}, {2, -3}, {2, -1}, {2, -19}, {2, 1}, {1, 16}, {2, -16}, {0, 6}, {2, 2}, {1, 8}}, {{1, 4}, {1, 9}, {1, 8}, {2, -12}, {0, 4}, {1, 8}, {0, 9}, {2, -2}, {2, -19}, {2, 2}, {2, -1}, {0, 14}, {2, 4}, {2, -17}, {0, 1}, {2, 4}, {2, -20}, {2, 3}, {0, 7}, {1, 4}}, {{0, 6}, {2, -5}, {1, 13}, {2, 15}, {2, 11}, {0, 7}, {1, 17}, {2, 9}, {1, 14}, {2, -7}, {2, 12}, {2, -18}, {0, 19}, {2, -1}, {2, 14}, {2, 5}, {2, -16}, {1, 2}, {2, -2}, {0, 17}}, {{1, 11}, {2, 4}, {2, 7}, {1, 16}, {2, 14}, {0, 14}, {2, 16}, {1, 11}, {1, 10}, {2, -3}, {2, -10}, {1, 7}, {2, 9}, {0, 19}, {2, 1}, {0, 7}, {1, 11}, {0, 9}, {2, -16}, {1, 8}}, {{0, 10}, {0, 4}, {2, -8}, {2, 20}, {2, 16}, {2, 5}, {0, 16}, {1, 6}, {2, 2}, {2, 14}, {2, 11}, {1, 15}, {2, -10}, {2, -5}, {0, 4}, {0, 4}, {2, -13}, {2, 11}, {0, 13}, {0, 11}}, {{0, 6}, {1, 4}, {2, 15}, {2, 17}, {1, 1}, {2, -20}, {1, 18}, {0, 19}, {2, -12}, {2, 1}, {2, -15}, {2, -11}, {1, 19}, {0, 13}, {1, 2}, {0, 17}, {2, 14}, {0, 14}, {2, 12}, {0, 19}}, {{2, -16}, {1, 20}, {2, -14}, {1, 7}, {2, -13}, {2, 19}, {2, 20}, {2, -14}, {1, 17}, {2, 20}, {1, 2}, {2, -19}, {2, -17}, {2, 18}, {2, 6}, {1, 17}, {2, 7}, {0, 8}, {1, 20}, {2, 9}},
+        {{2, 20}, {2, 17}, {2, 15}, {1, 13}, {0, 7}, {2, -6}, {0, 8}, {2, -17}, {1, 15}, {2, -20}, {0, 17}, {2, -17}, {0, 12}, {1, 14}, {2, -8}, {2, -17}, {0, 12}, {2, -3}, {2, -13}, {0, 7}}, {{0, 3}, {2, 12}, {2, 4}, {0, 13}, {0, 15}, {1, 4}, {2, 7}, {2, -20}, {0, 4}, {0, 6}, {0, 12}, {2, 10}, {2, -13}, {0, 20}, {2, -11}, {0, 16}, {2, -13}, {2, -5}, {1, 14}, {0, 7}}, {{2, 16}, {1, 11}, {2, -1}, {0, 9}, {0, 19}, {2, 9}, {2, 6}, {1, 15}, {2, 2}, {2, 8}, {1, 3}, {2, 20}, {2, -18}, {2, -15}, {2, -20}, {0, 10}, {1, 9}, {2, 5}, {2, -17}, {2, 14}}, {{2, -15}, {2, -10}, {2, -18}, {1, 20}, {1, 4}, {0, 18}, {1, 10}, {2, 19}, {2, -9}, {2, 20}, {0, 1}, {0, 11}, {2, -18}, {2, 5}, {1, 15}, {0, 10}, {2, -14}, {2, 6}, {0, 17}, {0, 3}}, {{1, 18}, {1, 5}, {0, 11}, {2, 11}, {0, 13}, {1, 5}, {0, 19}, {2, 20}, {1, 10}, {2, 19}, {0, 13}, {0, 7}, {2, 1}, {2, 14}, {1, 19}, {0, 9}, {1, 17}, {2, 18}, {0, 11}, {1, 9}}, {{2, -17}, {2, 10}, {2, -19}, {2, -18}, {2, 6}, {0, 9}, {0, 20}, {1, 7}, {2, -14}, {2, -11}, {0, 14}, {1, 1}, {0, 13}, {0, 2}, {2, 3}, {0, 2}, {2, 11}, {2, 10}, {2, 12}, {2, -4}}, {{2, 13}, {1, 14}, {2, 7}, {1, 12}, {2, -9}, {2, -4}, {2, -8}, {2, 13}, {0, 3}, {1, 20}, {2, 2}, {2, 5}, {0, 19}, {0, 10}, {2, 14}, {2, -15}, {1, 5}, {2, 18}, {2, -8}, {2, 6}}, {{1, 5}, {1, 9}, {1, 19}, {2, 19}, {0, 13}, {2, 2}, {2, 12}, {2, 17}, {2, -16}, {0, 12}, {0, 9}, {1, 17}, {0, 13}, {2, 7}, {1, 7}, {2, 14}, {0, 12}, {0, 7}, {2, -16}, {1, 7}}, {{2, 15}, {0, 9}, {1, 3}, {0, 4}, {2, -3}, {0, 12}, {2, 9}, {0, 6}, {1, 16}, {0, 10}, {2, -6}, {1, 20}, {2, 11}, {2, -3}, {2, -6}, {0, 15}, {0, 14}, {0, 11}, {2, -19}, {2, -14}}, {{0, 12}, {2, 8}, {1, 20}, {2, 18}, {2, 3}, {2, 2}, {2, 4}, {2, 7}, {2, -19}, {2, -9}, {2, 2}, {0, 19}, {0, 11}, {2, -9}, {0, 9}, {2, -14}, {1, 13}, {0, 2}, {0, 1}, {2, -19}},
+        {{2, -4}, {1, 6}, {0, 18}, {2, 4}, {1, 12}, {0, 17}, {2, 10}, {2, 13}, {2, 10}, {1, 10}, {2, -1}, {2, -11}, {2, -15}, {2, -5}, {2, -16}, {2, -12}, {0, 2}, {2, -10}, {2, 15}, {1, 2}}, {{2, -9}, {2, -14}, {1, 4}, {0, 5}, {2, -9}, {0, 7}, {0, 9}, {1, 16}, {1, 10}, {2, -14}, {0, 7}, {2, -18}, {0, 19}, {1, 3}, {1, 7}, {2, -19}, {2, 14}, {0, 9}, {1, 7}, {2, -5}}, {{2, 16}, {0, 13}, {2, 20}, {2, -9}, {0, 20}, {2, 20}, {0, 5}, {0, 6}, {1, 4}, {2, -11}, {0, 14}, {0, 9}, {2, 18}, {0, 14}, {0, 12}, {2, 16}, {2, 8}, {2, -13}, {1, 9}, {1, 3}}, {{2, 1}, {2, 13}, {2, -8}, {0, 9}, {2, -16}, {0, 12}, {0, 12}, {2, 19}, {2, -10}, {2, 1}, {2, -20}, {1, 10}, {0, 18}, {2, -15}, {2, -15}, {1, 15}, {0, 15}, {0, 1}, {2, -5}, {0, 19}}, {{2, 6}, {2, 15}, {2, -20}, {1, 20}, {2, 3}, {2, 7}, {1, 1}, {0, 5}, {0, 4}, {2, 8}, {1, 19}, {2, -3}, {2, 18}, {1, 10}, {0, 11}, {2, -19}, {0, 3}, {2, 5}, {1, 4}, {0, 6}}, {{0, 5}, {2, -17}, {1, 1}, {0, 1}, {2, -9}, {0, 8}, {2, -10}, {2, -4}, {0, 13}, {2, 19}, {0, 6}, {2, 9}, {2, 14}, {2, 11}, {0, 16}, {2, 13}, {1, 1}, {2, 9}, {2, 14}, {0, 18}}, {{0, 10}, {1, 12}, {1, 4}, {2, -12}, {2, 7}, {0, 5}, {1, 15}, {2, 7}, {2, 17}, {1, 18}, {2, 3}, {0, 12}, {1, 8}, {1, 13}, {2, -17}, {1, 20}, {0, 18}, {1, 12}, {1, 16}, {0, 16}}, {{2, -10}, {2, -1}, {2, 10}, {1, 4}, {2, -12}, {1, 19}, {2, 18}, {2, -15}, {2, -5}, {1, 11}, {2, -7}, {0, 20}, {2, -12}, {2, -12}, {1, 11}, {2, 8}, {2, 2}, {2, -2}, {2, -4}, {2, 19}}, {{2, 5}, {1, 15}, {1, 18}, {2, 20}, {1, 4}, {0, 7}, {2, -8}, {2, 1}, {2, -6}, {2, 8}, {1, 1}, {2, 12}, {1, 15}, {0, 16}, {1, 13}, {0, 1}, {0, 19}, {0, 20}, {2, -3}, {0, 12}}, {{1, 18}, {2, -4}, {1, 8}, {2, 19}, {1, 11}, {0, 12}, {0, 20}, {2, 4}, {1, 12}, {0, 17}, {2, 8}, {1, 5}, {2, -13}, {1, 3}, {1, 14}, {1, 4}, {0, 20}, {1, 18}, {0, 7}, {0, 17}},
+        {{2, 14}, {2, 10}, {2, -12}, {2, -15}, {1, 3}, {2, -17}, {1, 12}, {2, 9}, {2, -9}, {0, 11}, {2, 12}, {0, 16}, {0, 13}, {2, -17}, {2, 13}, {2, 11}, {1, 13}, {2, 16}, {0, 14}, {2, -8}}, {{0, 16}, {2, -10}, {1, 12}, {1, 12}, {2, 19}, {1, 5}, {2, 1}, {2, 19}, {0, 17}, {2, -19}, {2, 20}, {0, 7}, {1, 11}, {2, -3}, {2, -19}, {2, -20}, {2, 15}, {2, -18}, {2, 11}, {2, -19}}, {{2, -11}, {2, 10}, {0, 10}, {1, 15}, {1, 1}, {2, 7}, {2, -9}, {2, -3}, {0, 2}, {0, 20}, {0, 1}, {2, 14}, {2, -16}, {1, 14}, {0, 19}, {0, 11}, {2, 4}, {2, -9}, {2, -4}, {2, -10}}, {{2, 2}, {2, 17}, {1, 7}, {0, 18}, {0, 12}, {2, -15}, {2, 18}, {1, 7}, {1, 3}, {2, 14}, {1, 19}, {1, 6}, {2, -19}, {2, 9}, {0, 11}, {1, 13}, {2, -13}, {0, 19}, {1, 15}, {0, 14}}, {{2, 14}, {1, 3}, {2, 4}, {0, 14}, {1, 8}, {2, 7}, {0, 16}, {1, 11}, {2, 11}, {1, 13}, {1, 6}, {2, -10}, {0, 17}, {1, 18}, {1, 1}, {2, -11}, {1, 9}, {0, 16}, {2, 5}, {2, -6}}, {{0, 11}, {2, -2}, {1, 7}, {2, 8}, {2, 20}, {0, 7}, {0, 14}, {2, -17}, {2, 14}, {2, -14}, {2, -16}, {2, -12}, {2, -19}, {2, 10}, {2, -8}, {1, 1}, {1, 14}, {0, 5}, {0, 14}, {2, 14}}, {{2, 10}, {2, 18}, {1, 15}, {1, 15}, {2, 10}, {2, 14}, {1, 15}, {2, -16}, {2, -4}, {2, -1}, {2, -20}, {2, 2}, {1, 6}, {0, 2}, {2, -17}, {0, 13}, {2, -8}, {2, 18}, {2, 9}, {2, -12}}, {{2, -7}, {1, 16}, {2, 15}, {1, 14}, {1, 15}, {0, 8}, {1, 19}, {2, -13}, {2, 17}, {2, 4}, {2, -17}, {2, -2}, {0, 8}, {1, 11}, {2, 14}, {0, 13}, {2, -12}, {2, -1}, {2, -5}, {0, 6}}, {{0, 2}, {2, -1}, {2, -15}, {1, 9}, {0, 17}, {0, 8}, {2, 19}, {0, 5}, {1, 16}, {2, 3}, {1, 17}, {2, -8}, {2, -1}, {2, -4}, {2, -16}, {0, 4}, {2, -8}, {2, 14}, {2, -20}, {2, -15}}, {{0, 5}, {0, 20}, {1, 13}, {0, 13}, {2, 18}, {1, 19}, {0, 7}, {0, 13}, {2, -7}, {2, 11}, {0, 16}, {1, 6}, {2, -19}, {2, 6}, {1, 18}, {2, 4}, {2, -7}, {2, -8}, {2, 20}, {0, 19}}
+    };
+    // *INDENT-ON*
+
+    uint8_t buf[20];
+    uint8_t n = 0;
+    uint32_t bres = 0;
+    for(uint32_t i = 0; i < 100; i++) {
+        /* bring the pos back to the middle of the file */
+        int32_t pos = 500;
+        res = lv_fs_seek(&f, pos, LV_FS_SEEK_SET);
+        TEST_ASSERT_EQUAL(LV_FS_RES_OK, res);
+        for(uint32_t j = 0; j < 20; j++) {
+            int8_t action = actions[i][j][0];
+            int8_t amount = actions[i][j][1];
+            switch(action) {
+                case 0: /* read */
+                    res = lv_fs_read(&f, buf, amount, &bres);
+                    TEST_ASSERT_EQUAL(LV_FS_RES_OK, res);
+                    TEST_ASSERT_EQUAL(amount, bres);
+                    TEST_ASSERT(0 == memcmp(buf, buf1000 + pos, amount));
+                    pos += amount;
+                    break;
+                case 1: /* write */
+                    for(int32_t k = 0; k < amount; k++) {
+                        buf[k] = n;
+                        buf1000[pos + k] = n;
+                        n++;
+                    }
+                    res = lv_fs_write(&f, buf, amount, &bres);
+                    TEST_ASSERT_EQUAL(LV_FS_RES_OK, res);
+                    TEST_ASSERT_EQUAL(amount, bres);
+                    pos += amount;
+                    break;
+                case 2: /* seek */
+                    pos += amount; /* amount may be negative */
+                    res = lv_fs_seek(&f, pos, LV_FS_SEEK_SET);
+                    TEST_ASSERT_EQUAL(LV_FS_RES_OK, res);
+                    break;
+            }
+        }
+    }
+
+    /* test SEEK_END */
+    uint32_t tell_pos;
+    res = lv_fs_seek(&f, 0, LV_FS_SEEK_END);
+    TEST_ASSERT_EQUAL(LV_FS_RES_OK, res);
+    res = lv_fs_tell(&f, &tell_pos);
+    TEST_ASSERT_EQUAL(LV_FS_RES_OK, res);
+    TEST_ASSERT_EQUAL(tell_pos, 1000);
+
+    res = lv_fs_close(&f);
+    TEST_ASSERT_EQUAL(LV_FS_RES_OK, res);
+
+    drv->cache_size = original_cache_size;
+}
+
 #endif