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mirror of https://github.com/HDFGroup/hdf5.git synced 2025-03-31 17:10:47 +08:00

[svn-r22012] Purpose:

Task for HDFFV-7862 - Select data by chunk direction to improve performance in h5repack

Description:
  h5repack sometimes became very slow when handling big chunked datasets in
  certain cases. (when chunk boundary doesn't match with a hyperslab boundary.)
  The main issue was from figuring out a hypeslab without considering chunk
  boundary to read from and write to such datasets.
  The update was made to figure out a better hyperslab unit with considering
  chunk boundary to improve performance for such cases prior to the update.


Tested:
  jam (linux32-LE), koala (linux64-LE), ostrich (linuxppc64-BE), tejeda (mac32-LE), linew (solaris-BE), Windows
This commit is contained in:
Jonathan Kim 2012-03-01 17:59:46 -05:00
parent 196080ac0f
commit b994a10148
4 changed files with 483 additions and 265 deletions
release_docs
tools

@ -241,6 +241,12 @@ New Features
Tools:
------
- h5repack: Improved performance for hanlding big chunked dataset
(size > 128MB). It would perform much better prior to the
improvement, especially for cases that chunk dimentions
looks like "1024x5x1" (compare to "1x5x1024"). When bigger numbers
are toward front and smaller number is toward back in chunk
dimentions.
- h5dump: Added new option --no-compact-subset. This option will not
interpret the '[' character as starting the compact form of
subsetting. This is useful when the "h5dump error: unable to

@ -53,6 +53,7 @@
* local functions
*-------------------------------------------------------------------------
*/
static int Get_hyperslab (hid_t dcpl_id, int rank_dset, hsize_t dims_dset[], size_t size_datum, hsize_t dims_hslab[], hsize_t * hslab_nbytes_p);
static void print_dataset_info(hid_t dcpl_id,char *objname,double per, int pr);
static int do_copy_objects(hid_t fidin,hid_t fidout,trav_table_t *travt,pack_opt_t *options);
static int copy_user_block(const char *infile, const char *outfile, hsize_t size);
@ -490,6 +491,184 @@ out:
return -1;
}
/*-------------------------------------------------------------------------
* Function: Get_hyperslab
*
* Purpose: Calulate a hyperslab from a dataset for higher performance.
* The size of hyperslab is limitted by H5TOOLS_BUFSIZE.
* Return the hyperslab dimentions and size in byte.
*
* Return: 0 - SUCCEED, -1 FAILED
*
* Parameters:
* dcpl_id : [IN] dataset creation property.
* rank_dset : [IN] dataset rank
* dims_dset[] : [IN] dataset dimentions
* size_datum : [IN] size of a data element in byte
* dims_hslab[] : [OUT] calculated hyperslab dimentions
* * hslab_nbytes_p : [OUT] total byte of the hyperslab
*
* Programmer: Jonathan Kim
* Date: Feburary, 2012
* Update:
* The hyperslab calucation would be depend on if the dataset is chunked
* or not.
*
* There care 3 conditions to cover:
* 1. If chunked and a chunk fits in buffer, each chunk would be a unit of
* collection and the boundary would be dataset's dims.
* 2. If chunked but a chunk doesn't fit in buffer, each data element would
* be a unit of collection and the boundary would be the chunk itself.
* 3. If not chunked, each data element would be a unit of collection and
* the boundary would be dataset's dims.
*
* The calulation starts from the last dimention (h5dump dims output).
*
* Note:
* Added for JIRA HDFFV-7862.
*-----------------------------------------*/
int Get_hyperslab (hid_t dcpl_id, int rank_dset, hsize_t dims_dset[],
size_t size_datum,
hsize_t dims_hslab[], hsize_t * hslab_nbytes_p)
{
int status = 0;
int k;
H5D_layout_t dset_layout;
int rank_chunk;
hsize_t dims_chunk[H5S_MAX_RANK];
hsize_t size_chunk=1;
hsize_t nchunk_fit; /* number of chunks that fits in hyperslab buffer (H5TOOLS_BUFSIZE) */
hsize_t ndatum_fit; /* number of dataum that fits in hyperslab buffer (H5TOOLS_BUFSIZE) */
hsize_t chunk_dims_map[H5S_MAX_RANK]; /* mapped chunk dimentions */
hsize_t hs_dims_map[H5S_MAX_RANK]; /* mapped hyperslab dimentions */
hsize_t hslab_nbytes; /* size of hyperslab in byte */
/* init to set as size of a data element */
hslab_nbytes = size_datum;
/* get layout of dataset */
dset_layout = H5Pget_layout(dcpl_id);
/* if dataset is chunked */
if ( dset_layout == H5D_CHUNKED )
{
/* get chunk dims */
rank_chunk = H5Pget_chunk(dcpl_id, rank_dset, dims_chunk);
if (rank_chunk < 0)
{
status = -1;
goto out;
}
for (k = rank_dset; k > 0; --k)
size_chunk *= dims_chunk[k-1];
/* figure out how many chunks can fit in the hyperslab buffer */
nchunk_fit = (H5TOOLS_BUFSIZE / size_datum) / size_chunk;
/* 1. if a chunk fit in hyperslab buffer */
if (nchunk_fit >= 1)
{
/* Calulate a hyperslab that contains as many chunks that can fit
* in hyperslab buffer. Hyperslab will be increased starting from
* the last dimention of the dataset (see h5dump's dims output).
* The calculation boundary is dataset dims.
* In the loop, used mapping from a datum to a chunk to figure out
* chunk based hyperslab.
*/
for (k = rank_dset; k > 0; --k)
{
/* map dataset dimentions with a chunk dims */
chunk_dims_map[k-1]= dims_dset[k-1] / dims_chunk[k-1];
/* if reminder exist, increse by 1 to cover partial edge chunks */
if (dims_dset[k-1] % dims_chunk[k-1] > 0)
chunk_dims_map[k-1]++;
/* get mapped hyperslab dims */
hs_dims_map[k-1] = MIN (nchunk_fit, chunk_dims_map[k-1]);
/* prepare next round */
nchunk_fit = nchunk_fit / chunk_dims_map[k-1];
/* if a chunk is bigger than the rest of buffer */
if (nchunk_fit == 0)
nchunk_fit=1;
/* get hyperslab dimentions as unmapping to actual size */
dims_hslab[k-1] = MIN( (hs_dims_map[k-1] * dims_chunk[k-1]), dims_dset[k-1]);
/* calculate total size for the hyperslab */
hslab_nbytes *= dims_hslab[k-1];
}
}
/* 2. if a chunk is bigger than hyperslab buffer */
else
{
/* Calulate a hyperslab that contains as many data elements that
* can fit in hyperslab buffer. Hyperslab will be increased
* starting from the last dimention of the chunk (see h5dump's dims
* output).
* The calculation boundary is a chunk dims.
*/
for (k = rank_dset; k > 0; --k)
{
ndatum_fit = H5TOOLS_BUFSIZE / hslab_nbytes;
/* if a datum is bigger than rest of buffer */
if ( ndatum_fit == 0)
ndatum_fit = 1;
/* get hyperslab dimentions within a chunk boundary */
dims_hslab[k - 1] = MIN (dims_chunk[k-1], ndatum_fit);
/* calculate total size for the hyperslab */
hslab_nbytes *= dims_hslab[k - 1];
if (hslab_nbytes <= 0)
{
status = -1;
goto out;
}
}
}
}
/* 3. if dataset is not chunked */
else
{
/* Calulate a hyperslab that contains as many data elements that can
* fit in hyperslab buffer. Hyperslab will be increased starting from
* the last dimention of the dataset (see h5dump's dims output).
* The calculation boundary is dataset dims.
*/
for (k = rank_dset; k > 0; --k)
{
ndatum_fit = H5TOOLS_BUFSIZE / hslab_nbytes;
/* if a datum is bigger than rest of buffer */
if ( ndatum_fit == 0)
ndatum_fit = 1;
/* get hyperslab dimentions within dataset boundary */
dims_hslab[k - 1] = MIN(dims_dset[k - 1], ndatum_fit);
/* calculate total size for the hyperslab */
hslab_nbytes *= dims_hslab[k - 1];
if (hslab_nbytes <= 0)
{
status = -1;
goto out;
}
}
}
/* pass out the hyperslab size*/
*hslab_nbytes_p = hslab_nbytes;
out:
return status;
}
/*-------------------------------------------------------------------------
* Function: do_copy_objects
*
@ -557,6 +736,30 @@ out:
*
* May, 1, 2008: Add a printing of the compression ratio of old size / new size
*
* Feburary 2012: improve Read/Write by hyperslabs for big datasets.
* Programmer: Jonathan Kim
*
* A threshold of H5TOOLS_MALLOCSIZE is the limit upon which I/O hyperslab is done
* i.e., if the memory needed to read a dataset is greater than this limit,
* then hyperslab I/O is done instead of one operation I/O
* For each dataset, the memory needed is calculated according to
*
* memory needed = number of elements * size of each element
*
* if the memory needed is lower than H5TOOLS_MALLOCSIZE, then the following operations
* are done
*
* H5Dread( input_dataset )
* H5Dwrite( output_dataset )
*
* with all elements in the datasets selected. If the memory needed is greater than
* H5TOOLS_MALLOCSIZE, then the following operations are done instead:
*
* 1. figure out a hyperslab (dimentions) and size (refer to Get_hyperslab()).
* 2. Calculate the hyperslab selections as the selection is moving forward.
* Selection would be same as the hyperslab except for the remaining edge portion
* of the dataset. The code take care of the remaining portion if exist.
*
*-------------------------------------------------------------------------
*/
@ -573,7 +776,7 @@ int do_copy_objects(hid_t fidin,
hid_t gcpl_out = -1; /* group creation property list */
hid_t type_in = -1; /* named type ID */
hid_t type_out = -1; /* named type ID */
hid_t dcpl_id = -1; /* dataset creation property list ID */
hid_t dcpl_in = -1; /* dataset creation property list ID */
hid_t dcpl_out = -1; /* dataset creation property list ID */
hid_t f_space_id = -1; /* file space ID */
hid_t ftype_id = -1; /* file type ID */
@ -589,7 +792,7 @@ int do_copy_objects(hid_t fidin,
int apply_s; /* flag for apply filter to small dataset sizes */
int apply_f; /* flag for apply filter to return error on H5Dcreate */
void *buf=NULL; /* buffer for raw data */
void *sm_buf=NULL; /* buffer for raw data */
void *hslab_buf=NULL; /* hyperslab buffer for raw data */
int has_filter; /* current object has a filter */
int req_filter; /* there was a request for a filter */
unsigned crt_order_flags; /* group creation order flag */
@ -598,6 +801,7 @@ int do_copy_objects(hid_t fidin,
int is_ref=0;
htri_t is_named;
/*-------------------------------------------------------------------------
* copy the suppplied object list
*-------------------------------------------------------------------------
@ -760,9 +964,9 @@ int do_copy_objects(hid_t fidin,
goto error;
if((ftype_id = H5Dget_type(dset_in)) < 0)
goto error;
if((dcpl_id = H5Dget_create_plist(dset_in)) < 0)
if((dcpl_in = H5Dget_create_plist(dset_in)) < 0)
goto error;
if((dcpl_out = H5Pcopy(dcpl_id)) < 0)
if((dcpl_out = H5Pcopy(dcpl_in)) < 0)
goto error;
if((rank = H5Sget_simple_extent_ndims(f_space_id)) < 0)
goto error;
@ -795,7 +999,7 @@ int do_copy_objects(hid_t fidin,
* 2) the internal filters might be turned off
*-------------------------------------------------------------------------
*/
if (h5tools_canreadf((travt->objs[i].name),dcpl_id)==1)
if (h5tools_canreadf((travt->objs[i].name),dcpl_in)==1)
{
apply_s=1;
apply_f=1;
@ -855,7 +1059,7 @@ int do_copy_objects(hid_t fidin,
printf(" warning: could not create dataset <%s>. Applying original settings\n",
travt->objs[i].name);
if((dset_out = H5Dcreate2(fidout, travt->objs[i].name, wtype_id, f_space_id, H5P_DEFAULT, dcpl_id, H5P_DEFAULT)) < 0)
if((dset_out = H5Dcreate2(fidout, travt->objs[i].name, wtype_id, f_space_id, H5P_DEFAULT, dcpl_in, H5P_DEFAULT)) < 0)
goto error;
apply_f = 0;
}
@ -886,100 +1090,108 @@ int do_copy_objects(hid_t fidin,
else /* possibly not enough memory, read/write by hyperslabs */
{
size_t p_type_nbytes = msize; /*size of memory type */
hsize_t p_nelmts = nelmts; /*total selected elmts */
hsize_t p_nelmts = nelmts; /*total elements */
hsize_t elmtno; /*counter */
int carry; /*counter carry value */
unsigned int vl_data = 0; /*contains VL datatypes */
/* stripmine info */
hsize_t sm_size[H5S_MAX_RANK]; /*stripmine size */
hsize_t sm_nbytes; /*bytes per stripmine */
hsize_t sm_nelmts; /*elements per stripmine*/
hid_t sm_space; /*stripmine data space */
/* hyperslab info */
hsize_t hs_offset[H5S_MAX_RANK];/*starting offset */
hsize_t hs_size[H5S_MAX_RANK]; /*size this pass */
hsize_t hs_nelmts; /*elements in request */
hsize_t hslab_dims[H5S_MAX_RANK]; /*hyperslab dims */
hsize_t hslab_nbytes; /*bytes per hyperslab */
hsize_t hslab_nelmts; /*elements per hyperslab*/
hid_t hslab_space; /*hyperslab data space */
/* hyperslab selection info */
hsize_t hs_sel_offset[H5S_MAX_RANK];/* selection offset */
hsize_t hs_sel_count[H5S_MAX_RANK]; /* selection count */
hsize_t hs_select_nelmts; /* selected elements */
hsize_t zero[8]; /*vector of zeros */
int k;
H5D_layout_t dset_layout;
hid_t dcpl_tmp = -1; /* dataset creation property list ID */
/* check if we have VL data in the dataset's datatype */
if (H5Tdetect_class(wtype_id, H5T_VLEN) == TRUE)
vl_data = TRUE;
/*
* determine the strip mine size and allocate a buffer. The strip mine is
* a hyperslab whose size is manageable.
*/
sm_nbytes = p_type_nbytes;
for (k = rank; k > 0; --k)
/* check first if writing dataset is chunked,
* if so use its chunk layout for better performance. */
dset_layout = H5Pget_layout(dcpl_out);
if (dset_layout == H5D_CHUNKED)
dcpl_tmp = dcpl_out; /* writing dataset */
else /* if reading dataset is chunked */
{
hsize_t size = H5TOOLS_BUFSIZE / sm_nbytes;
if ( size == 0) /* datum size > H5TOOLS_BUFSIZE */
size = 1;
sm_size[k - 1] = MIN(dims[k - 1], size);
sm_nbytes *= sm_size[k - 1];
HDassert(sm_nbytes > 0);
dset_layout = H5Pget_layout(dcpl_in);
if (dset_layout == H5D_CHUNKED)
dcpl_tmp = dcpl_in; /* reading dataset */
}
sm_buf = HDmalloc((size_t)sm_nbytes);
sm_nelmts = sm_nbytes / p_type_nbytes;
sm_space = H5Screate_simple(1, &sm_nelmts, NULL);
/* get hyperslab dims and size in byte */
if(Get_hyperslab(dcpl_tmp, rank, dims, p_type_nbytes, hslab_dims, &hslab_nbytes) < 0)
goto error;
/* the stripmine loop */
HDmemset(hs_offset, 0, sizeof hs_offset);
hslab_buf = HDmalloc((size_t)hslab_nbytes);
hslab_nelmts = hslab_nbytes / p_type_nbytes;
hslab_space = H5Screate_simple(1, &hslab_nelmts, NULL);
/* the hyperslab selection loop */
HDmemset(hs_sel_offset, 0, sizeof hs_sel_offset);
HDmemset(zero, 0, sizeof zero);
for (elmtno = 0; elmtno < p_nelmts; elmtno += hs_nelmts)
for (elmtno = 0; elmtno < p_nelmts; elmtno += hs_select_nelmts)
{
/* calculate the hyperslab size */
if (rank > 0)
{
for (k = 0, hs_nelmts = 1; k < rank; k++)
/* calculate the hyperslab selections. The selection would be same as the hyperslab except for remaining edge portion of the dataset which is smaller then the hyperslab.
*/
for (k = 0, hs_select_nelmts = 1; k < rank; k++)
{
hs_size[k] = MIN(dims[k] - hs_offset[k], sm_size[k]);
hs_nelmts *= hs_size[k];
/* MIN() is used to get the remaining edge portion if exist.
* "dims[k] - hs_sel_offset[k]" is remaining edge portion that is smaller then the hyperslab.*/
hs_sel_count[k] = MIN(dims[k] - hs_sel_offset[k], hslab_dims[k]);
hs_select_nelmts *= hs_sel_count[k];
}
if (H5Sselect_hyperslab(f_space_id, H5S_SELECT_SET, hs_offset, NULL, hs_size, NULL) < 0)
if (H5Sselect_hyperslab(f_space_id, H5S_SELECT_SET, hs_sel_offset, NULL, hs_sel_count, NULL) < 0)
goto error;
if (H5Sselect_hyperslab(sm_space, H5S_SELECT_SET, zero, NULL, &hs_nelmts, NULL) < 0)
if (H5Sselect_hyperslab(hslab_space, H5S_SELECT_SET, zero, NULL, &hs_select_nelmts, NULL) < 0)
goto error;
}
else
{
H5Sselect_all(f_space_id);
H5Sselect_all(sm_space);
hs_nelmts = 1;
H5Sselect_all(hslab_space);
hs_select_nelmts = 1;
} /* rank */
/* read/write: use the macro to check error, e.g. memory allocation error inside the library. */
CHECK_H5DRW_ERROR(H5Dread, dset_in, wtype_id, sm_space, f_space_id, H5P_DEFAULT, sm_buf);
CHECK_H5DRW_ERROR(H5Dwrite, dset_out, wtype_id, sm_space, f_space_id, H5P_DEFAULT, sm_buf);
CHECK_H5DRW_ERROR(H5Dread, dset_in, wtype_id, hslab_space, f_space_id, H5P_DEFAULT, hslab_buf);
CHECK_H5DRW_ERROR(H5Dwrite, dset_out, wtype_id, hslab_space, f_space_id, H5P_DEFAULT, hslab_buf);
/* reclaim any VL memory, if necessary */
if(vl_data)
H5Dvlen_reclaim(wtype_id, sm_space, H5P_DEFAULT, sm_buf);
H5Dvlen_reclaim(wtype_id, hslab_space, H5P_DEFAULT, hslab_buf);
/* calculate the next hyperslab offset */
for (k = rank, carry = 1; k > 0 && carry; --k)
{
hs_offset[k - 1] += hs_size[k - 1];
if (hs_offset[k - 1] == dims[k - 1])
hs_offset[k - 1] = 0;
hs_sel_offset[k - 1] += hs_sel_count[k - 1];
/* if reached the end of a dim */
if (hs_sel_offset[k - 1] == dims[k - 1])
hs_sel_offset[k - 1] = 0;
else
carry = 0;
} /* k */
} /* elmtno */
H5Sclose(sm_space);
H5Sclose(hslab_space);
/* free */
if (sm_buf!=NULL)
if (hslab_buf!=NULL)
{
HDfree(sm_buf);
sm_buf=NULL;
HDfree(hslab_buf);
hslab_buf=NULL;
}
} /* hyperslab read */
} /* if (nelmts>0 && space_status==H5D_SPACE_STATUS_NOT_ALLOCATED) */
@ -1005,7 +1217,7 @@ int do_copy_objects(hid_t fidin,
print_dataset_info(dcpl_out,travt->objs[i].name,ratio,1);
}
else
print_dataset_info(dcpl_id,travt->objs[i].name,ratio,0);
print_dataset_info(dcpl_in,travt->objs[i].name,ratio,0);
/* print a message that the filter was not applied
(in case there was a filter)
@ -1044,7 +1256,7 @@ int do_copy_objects(hid_t fidin,
goto error;
if (H5Tclose(wtype_id) < 0)
goto error;
if (H5Pclose(dcpl_id) < 0)
if (H5Pclose(dcpl_in) < 0)
goto error;
if (H5Pclose(dcpl_out) < 0)
goto error;
@ -1199,7 +1411,7 @@ error:
H5E_BEGIN_TRY {
H5Gclose(grp_in);
H5Gclose(grp_out);
H5Pclose(dcpl_id);
H5Pclose(dcpl_in);
H5Pclose(gcpl_in);
H5Pclose(gcpl_out);
H5Sclose(f_space_id);
@ -1214,8 +1426,8 @@ error:
/* free */
if (buf!=NULL)
HDfree(buf);
if (sm_buf!=NULL)
HDfree(sm_buf);
if (hslab_buf!=NULL)
HDfree(hslab_buf);
return -1;
}

@ -49,9 +49,9 @@ static const char *h5tools_progname = "h5tools";
* largest value suitable for your machine (for testing use a small value).
*/
/* Maximum size used in a call to malloc for a dataset */
hsize_t H5TOOLS_MALLOCSIZE = (128 * 1024 * 1024);
hsize_t H5TOOLS_MALLOCSIZE = (256 * 1024 * 1024); /* 256 MB */
/* size of hyperslab buffer when a dataset is bigger than H5TOOLS_MALLOCSIZE */
hsize_t H5TOOLS_BUFSIZE = (1024 * 1024);
hsize_t H5TOOLS_BUFSIZE = ( 32 * 1024 * 1024); /* 32 MB */
/* ``parallel_print'' variables */

@ -6338,212 +6338,212 @@ GROUP "/" {
(30,4025): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
(30,4045): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
(30,4065): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
(30,4085): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
(31,8): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
(31,29): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
(31,50): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
(31,71): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
(31,92): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
(31,113): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
(31,133): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
(31,153): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
(31,173): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
(31,193): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
(31,213): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
(31,233): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
(31,253): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
(31,273): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
(31,293): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
(31,313): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
(31,333): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
(31,353): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
(31,373): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
(31,393): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
(31,413): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
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