From 185cc9746b5fa539f68f4a16800e34e773fe02d7 Mon Sep 17 00:00:00 2001 From: Jonathan Kim Date: Tue, 6 Mar 2012 10:41:55 -0500 Subject: [svn-r22031] 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 --- release_docs/RELEASE.txt | 5 +- tools/h5repack/h5repack_copy.c | 326 ++++++++++++++++++++++++++------ tools/lib/h5tools_utils.c | 4 +- tools/testfiles/thyperslab.ddl | 412 ++++++++++++++++++++--------------------- 4 files changed, 481 insertions(+), 266 deletions(-) diff --git a/release_docs/RELEASE.txt b/release_docs/RELEASE.txt index 3beb250..d8124db 100644 --- a/release_docs/RELEASE.txt +++ b/release_docs/RELEASE.txt @@ -68,7 +68,10 @@ New Features Tools ----- - - None + - h5repack: Improved performance for hanlding big chunked datasets (size > 128MB). + Especially performance would be much better prior to the update, for the cases + that chunk dimentions look like "1024x5x1" (opposite to "1x5x1024"). When big + numbers are toward front and small numbers are toward back in chunk dimentions. High-Level APIs --------------- diff --git a/tools/h5repack/h5repack_copy.c b/tools/h5repack/h5repack_copy.c index 62cdd6b..ff682a2 100644 --- a/tools/h5repack/h5repack_copy.c +++ b/tools/h5repack/h5repack_copy.c @@ -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); @@ -447,6 +448,184 @@ out: } /*------------------------------------------------------------------------- +* 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 * * Purpose: duplicate all HDF5 objects in the file @@ -513,6 +692,30 @@ 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. +* *------------------------------------------------------------------------- */ @@ -529,7 +732,7 @@ 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 */ @@ -545,7 +748,7 @@ 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 */ @@ -554,6 +757,7 @@ int do_copy_objects(hid_t fidin, int is_ref=0; htri_t is_named; + /*------------------------------------------------------------------------- * copy the suppplied object list *------------------------------------------------------------------------- @@ -716,9 +920,9 @@ 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; @@ -751,7 +955,7 @@ 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; @@ -811,7 +1015,7 @@ 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; } @@ -842,100 +1046,108 @@ 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; + + hslab_buf = HDmalloc((size_t)hslab_nbytes); + + hslab_nelmts = hslab_nbytes / p_type_nbytes; + hslab_space = H5Screate_simple(1, &hslab_nelmts, NULL); - /* the stripmine loop */ - HDmemset(hs_offset, 0, sizeof hs_offset); + /* 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) */ @@ -961,7 +1173,7 @@ 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) @@ -1000,7 +1212,7 @@ 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; @@ -1155,7 +1367,7 @@ 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); @@ -1170,8 +1382,8 @@ error: /* free */ if (buf!=NULL) HDfree(buf); - if (sm_buf!=NULL) - HDfree(sm_buf); + if (hslab_buf!=NULL) + HDfree(hslab_buf); return -1; } diff --git a/tools/lib/h5tools_utils.c b/tools/lib/h5tools_utils.c index 4505609..11ab5f3 100644 --- a/tools/lib/h5tools_utils.c +++ b/tools/lib/h5tools_utils.c @@ -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 */ diff --git a/tools/testfiles/thyperslab.ddl b/tools/testfiles/thyperslab.ddl index cfebd14..2f4a118 100644 --- a/tools/testfiles/thyperslab.ddl +++ b/tools/testfiles/thyperslab.ddl @@ -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, - (31,433): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,453): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,473): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,493): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,513): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,533): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,553): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,573): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,593): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,613): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,633): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,653): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,673): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,693): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,713): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,733): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,753): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,773): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,793): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,813): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,833): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,853): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,873): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,893): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,913): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,933): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,953): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,973): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,993): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,1013): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,1033): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,1053): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,1073): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,1093): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,1113): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,1133): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,1153): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,1173): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,1193): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,1213): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,1233): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,1253): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,1273): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,1293): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,1313): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,1333): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,1353): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,1373): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,1393): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,1413): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,1433): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,1453): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,1473): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,1493): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,1513): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,1533): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,1553): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,1573): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,1593): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,1613): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,1633): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,1653): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,1673): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,1693): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,1713): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,1733): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,1753): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,1773): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,1793): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,1813): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,1833): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,1853): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,1873): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,1893): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,1913): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,1933): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,1953): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,1973): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,1993): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,2013): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,2033): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,2053): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,2073): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,2093): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,2113): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,2133): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,2153): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,2173): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,2193): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,2213): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,2233): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,2253): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,2273): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,2293): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,2313): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,2333): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,2353): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,2373): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,2393): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,2413): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,2433): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,2453): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,2473): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,2493): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,2513): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,2533): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,2553): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,2573): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - (31,2593): 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - 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