Coding and modulation apparatus using non-uniform constellation
A coding and modulation apparatus and method are presented. The apparatus comprises an encoder that encodes input data into cell words, and a modulator that modulates said cell words into constellation values of a non-uniform constellation. The modulator is configured to use, based on the total number M of constellation points of the constellation and the code rate, a non-uniform constellation from one or several groups of constellations each comprising one or more constellations.
1. A receiving apparatus comprising:
a receiver configured to receive at least one transmission stream including symbols representative of constellation values; and
at least one processor configured to demodulate the symbols into cell words associated with Low Density Parity Check (LDPC) codewords; wherein
each of the symbols is associated with a point of a NUC, Non-Uniform Constellation,
the NUC includes sixteen points;
the NUC includes complex points defined by their real and imaginary parts as:
0.9555+j0.9555
0.9555+j0.2949
0.2949+j0.9555
0.2949+j0.2949;
and wherein a code rate of the LDPC is 12/15.
2. The receiving apparatus according to claim 1 , wherein a first quarter of the NUC includes complex points defined by their real and imaginary parts as:
0.9555+j0.9555
0.9555+j0.2949
0.2949+j0.9555
0.2949+j0.2949;
a second quarter of the NUC includes points, each being an opposite of a complex conjugate of a point of the first quarter;
a third quarter of the NUC includes points, each being a complex conjugate of a point of the first quarter; and
a fourth quarter of the NUC includes points, each being an opposite of a point of the first quarter.
3. The receiving apparatus according to claim 1 , wherein the at least one transmission stream is a digital video broadcasting stream.
4. The receiving apparatus according to claim 1 , wherein the at least one processor is configured to decode the cell words into output data.
5. The receiving apparatus according to claim 1 , wherein
the LDPC has a code length of 64800 bits and is associated with a parity check matrix initial value table showing positions of elements corresponding to the value “1” in an information matrix portion in units of 360 columns and
wherein the parity check matrix initial value table includes:
584 1472 1621 1867 3338 3568 3723 4185 5126 5889 7737 8632
8940 9725 221 445 590 3779 3835 6939 7743 8280 8448 8491
9367 10042 11242 12917 4662 4837 4900 5029 6449 6687 6751
8684 9936 11681 11811 11886 12089 12909 2418 3018 3647
4210 4473 7447 7502 9490 10067 11092 11139 11256 12201
12383 2591 2947 3349 3406 4417 4519 5176 6672 8498 8863
9201 11294 11376 12184 27 101 197 290 871 1727 3911 5411
6676 8701 9350 10310 10798 12439 1765 1897 2923 3584 3901
4048 6963 7054 7132 9165 10184 10824 11278 12669 2183 3740
4808 5217 5660 6375 6787 8219 8466 9037 10353 10583 11118
12762 73 1594 2146 2715 3501 3572 3639 3725 6959 7187 8406
10120 10507 10691 240 732 1215 2185 2788 2830 3499 3881 4197
4991 6425 7061 9756 10491 831 1568 1828 3424 4319 4516 4639
6018 9702 10203 10417 11240 11518 12458 2024 2970 3048 3638
3676 4152 5284 5779 5926 9426 9945 10873 11787 11837 1049
1218 1651 2328 3493 4363 5750 6483 7613 8782 9738 9803 11744
11937 1193 2060 2289 2964 3478 4592 4756 6709 7162 8231 8326
11140 11908 12243 978 2120 2439 3338 3850 4589 6567 8745 9656
9708 10161 10542 10711 12639 2403 2938 3117 3247 3711 5593
5844 5932 7801 10152 10226 11498 12162 12941 1781 2229 2276
2533 3582 3951 5279 5774 7930 9824 10920 11038 12340 12440
289 384 1980 2230 3464 3873 5958 8656 8942 9006 10175 11425
11745 12530 155 354 1090 1330 2002 2236 3559 3705 4922 5958
6576 8564 9972 12760 303 876 2059 2142 5244 5330 6644 7576
8614 9598 10410 10718 11033 12957 3449 3617 4408 4602 4727
6182 8835 8928 9372 9644 10237 10747 11655 12747 811 2565
2820 8677 8974 9632 11069 11548 11839 12107 12411 12695
12812 12890 972 4123 4943 6385 6449 7339 7477 8379 9177
9359 10074 11709 12552 12831 842 973 1541 2262 2905 5276
6758 7099 7894 8128 8325 8663 8875 10050 474 791 968 3902
4924 4965 5085 5908 6109 6329 7931 9038 9401 10568 1397
4461 4658 5911 6037 7127 7318 8678 8924 9000 9473 9602
10446 12692
1334 7571 12881
1393 1447 7972
633 1257 10597
4843 5102 11056
3294 8015 10513
1108 10374 10546
5353 7824 10111
3398 7674 8569
7719 9478 10503
2997 9418 9581
5777 6519 11229
1966 5214 9899
6 4088 5827
836 9248 9612
483 7229 7548
7865 8289 9804
2915 11098 11900
6180 7096 9481
1431 6786 8924
748 6757 8625
3312 4475 7204
1852 8958 11020
1915 2903 4006
6776 10886 12531
2594 9998 12742
159 2002 12079
853 3281 3762
5201 5798 6413
3882 6062 12047
4133 6775 9657
228 6874 11183
7433 10728 10864
7735 8073 12734
2844 4621 11779
3909 7103 12804
6002 9704 11060
5864 6856 7681
3652 5869 7605
2546 2657 4461
2423 4203 9111
244 1855 4691
1106 2178 6371
391 1617 10126
250 9259 10603
3435 4614 6924
1742 8045 9529
7667 8875 11451
4023 6108 6911
8621 10184 11650
6726 10861 12348
3228 6302 7388
1 1137 5358
381 2424 8537
3256 7508 10044
1980 2219 4569
2468 5699 10319
2803 3314 12808
8578 9642 11533
829 4585 7923
59 329 5575
1067 5709 6867
1175 4744 12219
109 2518 6756
2105 10626 11153
5192 10696 10749
6260 7641 8233
2998 3094 11214
3398 6466 11494
6574 10448 12160
2734 10755 12780
1028 7958 10825
8545 8602 10793
392 3398 11417
6639 9291 12571
1067 7919 8934
1064 2848 12753
6076 8656 12690
5504 6193 10171
1951 7156 7356
4389 4780 7889
526 4804 9141
1238 3648 10464
2587 5624 12557
5560 5903 11963
1134 2570 3297
10041 11583 12157
1263 9585 12912
3744 7898 10646
45 9074 10315
1051 6188 10038
2242 8394 12712
3598 9025 12651
2295 3540 5610
1914 4378 12423
1766 3635 12759
5177 9586 11143
943 3590 11649
4864 6905 10454
5852 6042 10421
6095 8285 12349
2070 7171 8563
718 12234 12716
512 10667 11353
3629 6485 7040
2880 8865 11466
4490 10220 11796
5440 8819 9103
5262 7543 12411
516 7779 10940
2515 5843 9202
4684 5994 10586
573 2270 3324
7870 8317 10322
6856 7638 12909
1583 7669 10781
8141 9085 12555
3903 5485 9992
4467 11998 12904.
6. A receiving method comprising:
receiving at least one transmission stream including symbols representative of constellation values;
demodulating the symbols into cell words associated with Low Density Parity Check (LDPC) codewords, wherein
each of the symbols is associated with a point of a NUC, Non-Uniform Constellation,
the NUC includes sixteen points;
the NUC includes complex points defined by their real and imaginary parts as:
0.9555+j0.9555
0.9555+j0.2949
0.2949+j0.9555
0.2949+j0.2949,
and wherein a code rate of the LDPC is 12/15.
7. The receiving method according to claim 6 , wherein a first quarter of the NUC includes complex points defined by their real and imaginary parts as:
0.9555+j0.9555
0.9555+j0.2949
0.2949+j0.9555
0.2949+j0.2949;
a second quarter of the NUC includes points, each being an opposite of a complex conjugate of a point of the first quarter;
a third quarter of the NUC includes points, each being a complex conjugate of a point of the first quarter; and
a fourth quarter of the NUC includes points, each being an opposite of a point of the first quarter.
8. The receiving method according to claim 6 , wherein the at least one transmission stream is a digital video broadcasting stream.
9. The receiving method according to claim 6 , further comprising decoding the cell words into output data.
10. The receiving method according to claim 6 , wherein
the LDPC has a code length of 64800 bits and is associated with a parity check matrix initial value table showing positions of elements corresponding to the value “1” in an information matrix portion in units of 360 columns and
wherein the parity check matrix initial value table includes:
584 1472 1621 1867 3338 3568 3723 4185 5126 5889 7737 8632
8940 9725 221 445 590 3779 3835 6939 7743 8280 8448 8491 9367
10042 11242 12917 4662 4837 4900 5029 6449 6687 6751 8684
9936 11681 11811 11886 12089 12909 2418 3018 3647 4210 4473
7447 7502 9490 10067 11092 11139 11256 12201 12383 2591 2947
3349 3406 4417 4519 5176 6672 8498 8863 9201 11294 11376
12184 27 101 197 290 871 1727 3911 5411 6676 8701 9350 10310
10798 12439 1765 1897 2923 3584 3901 4048 6963 7054 7132
9165 10184 10824 11278 12669 2183 3740 4808 5217 5660 6375
6787 8219 8466 9037 10353 10583 11118 12762 73 1594 2146
2715 3501 3572 3639 3725 6959 7187 8406 10120 10507 10691
240 732 1215 2185 2788 2830 3499 3881 4197 4991 6425 7061
9756 10491 831 1568 1828 3424 4319 4516 4639 6018 9702 10203
10417 11240 11518 12458 2024 2970 3048 3638 3676 4152 5284
5779 5926 9426 9945 10873 11787 11837 1049 1218 1651 2328
3493 4363 5750 6483 7613 8782 9738 9803 11744 11937 1193
2060 2289 2964 3478 4592 4756 6709 7162 8231 8326 11140
11908 12243 978 2120 2439 3338 3850 4589 6567 8745 9656 9708
10161 10542 10711 12639 2403 2938 3117 3247 3711 5593 5844
5932 7801 10152 10226 11498 12162 12941 1781 2229 2276 2533
3582 3951 5279 5774 7930 9824 10920 11038 12340 12440 289
384 1980 2230 3464 3873 5958 8656 8942 9006 10175 11425
11745 12530 155 354 1090 1330 2002 2236 3559 3705 4922 5958
6576 8564 9972 12760 303 876 2059 2142 5244 5330 6644 7576
8614 9598 10410 10718 11033 12957 3449 3617 4408 4602 4727
6182 8835 8928 9372 9644 10237 10747 11655 12747 811 2565
2820 8677 8974 9632 11069 11548 11839 12107 12411 12695
12812 12890 972 4123 4943 6385 6449 7339 7477 8379 9177 9359
10074 11709 12552 12831 842 973 1541 2262 2905 5276 6758
7099 7894 8128 8325 8663 8875 10050 474 791 968 3902 4924
4965 5085 5908 6109 6329 7931 9038 9401 10568 1397 4461 4658
5911 6037 7127 7318 8678 8924 9000 9473 9602 10446 12692
1334 7571 12881
1393 1447 7972
633 1257 10597
4843 5102 11056
3294 8015 10513
1108 10374 10546
5353 7824 10111
3398 7674 8569
7719 9478 10503
2997 9418 9581
5777 6519 11229
1966 5214 9899
6 4088 5827
836 9248 9612
483 7229 7548
7865 8289 9804
2915 11098 11900
6180 7096 9481
1431 6786 8924
748 6757 8625
3312 4475 7204
1852 8958 11020
1915 2903 4006
6776 10886 12531
2594 9998 12742
159 2002 12079
853 3281 3762
5201 5798 6413
3882 6062 12047
4133 6775 9657
228 6874 11183
7433 10728 10864
7735 8073 12734
2844 4621 11779
3909 7103 12804
6002 9704 11060
5864 6856 7681
3652 5869 7605
2546 2657 4461
2423 4203 9111
244 1855 4691
1106 2178 6371
391 1617 10126
250 9259 10603
3435 4614 6924
1742 8045 9529
7667 8875 11451
4023 6108 6911
8621 10184 11650
6726 10861 12348
3228 6302 7388
1 1137 5358
381 2424 8537
3256 7508 10044
1980 2219 4569
2468 5699 10319
2803 3314 12808
8578 9642 11533
829 4585 7923
59 329 5575
1067 5709 6867
1175 4744 12219
109 2518 6756
2105 10626 11153
5192 10696 10749
6260 7641 8233
2998 3094 11214
3398 6466 11494
6574 10448 12160
2734 10755 12780
1028 7958 10825
8545 8602 10793
392 3398 11417
6639 9291 12571
1067 7919 8934
1064 2848 12753
6076 8656 12690
5504 6193 10171
1951 7156 7356
4389 4780 7889
526 4804 9141
1238 3648 10464
2587 5624 12557
5560 5903 11963
1134 2570 3297
10041 11583 12157
1263 9585 12912
3744 7898 10646
45 9074 10315
1051 6188 10038
2242 8394 12712
3598 9025 12651
2295 3540 5610
1914 4378 12423
1766 3635 12759
5177 9586 11143
943 3590 11649
4864 6905 10454
5852 6042 10421
6095 8285 12349
2070 7171 8563
718 12234 12716
512 10667 11353
3629 6485 7040
2880 8865 11466
4490 10220 11796
5440 8819 9103
5262 7543 12411
516 7779 10940
2515 5843 9202
4684 5994 10586
573 2270 3324
7870 8317 10322
6856 7638 12909
1583 7669 10781
8141 9085 12555
3903 5485 9992
4467 11998 12904.
11. A receiver configured to receive at least one transmission stream including symbols representative of constellation values; and
at least one processor configured to demodulate the symbols into cell words associated with Low Density Parity Check (LDPC) codewords; wherein
each of the symbols is associated with a point of a NUC, Non-Uniform Constellation,
the NUC includes sixty-four points;
the NUC includes complex points defined by their real and imaginary parts as:
1.4480+j0.2403
0.6406+j1.1995
1.0952+j0.9115
0.6868+j0.8108
1.0500+j0.1642
0.7170+j0.1473
1.0519+j0.5188
0.7146+j0.4532
0.1677+j1.0405
0.2402+j1.4087
0.1369+j0.7073
0.4044+j0.7057
0.1374+j0.1295
0.4185+j0.1357
0.1325+j0.3998
0.4122+j0.4120;
and wherein a code rate of the LDPC is 12/15.
12. The receiving apparatus according to claim 11 , wherein a first quarter of the NUC includes complex points defined by their real and imaginary parts as:
1.4480+j0.2403
0.6406+j1.1995
1.0952+j0.9115
0.6868+j0.8108
1.0500+j0.1642
0.7170+j0.1473
1.0519+j0.5188
0.7146+j0.4532
0.1677+j1.0405
0.2402+j1.4087
0.1369+j0.7073
0.4044+j0.7057
0.1374+j0.1295
0.4185+j0.1357
0.1325+j0.3998
0.4122+j0.4120;
a second quarter of the NUC includes points, each being an opposite of a complex conjugate of a point of the first quarter;
a third quarter of the NUC includes points, each being a complex conjugate of a point of the first quarter; and
a fourth quarter of the NUC includes points, each being an opposite of a point of the first quarter.
13. The receiving apparatus according to claim 11 , wherein the at least one transmission stream is a digital video broadcasting stream.
14. The receiving apparatus according to claim 11 , wherein the at least one processor is configured to decode the cell words into output data.
15. The receiving apparatus according to claim 11 , wherein
the LDPC has a code length of 64800 bits and is associated with a parity check matrix initial value table showing positions of elements corresponding to the value “1” in an information matrix portion in units of 360 columns and
wherein the parity check matrix initial value table includes:
584 1472 1621 1867 3338 3568 3723 4185 5126 5889 7737 8632
8940 9725 221 445 590 3779 3835 6939 7743 8280 8448 8491
9367 10042 11242 12917 4662 4837 4900 5029 6449 6687 6751
8684 9936 11681 11811 11886 12089 12909 2418 3018 3647
4210 4473 7447 7502 9490 10067 11092 11139 11256 12201
12383 2591 2947 3349 3406 4417 4519 5176 6672 8498 8863
9201 11294 11376 12184 27 101 197 290 871 1727 3911 5411
6676 8701 9350 10310 10798 12439 1765 1897 2923 3584 3901
4048 6963 7054 7132 9165 10184 10824 11278 12669 2183 3740
4808 5217 5660 6375 6787 8219 8466 9037 10353 10583 11118
12762 73 1594 2146 2715 3501 3572 3639 3725 6959 7187 8406
10120 10507 10691 240 732 1215 2185 2788 2830 3499 3881
4197 4991 6425 7061 9756 10491 831 1568 1828 3424 4319
4516 4639 6018 9702 10203 10417 11240 11518 12458 2024
2970 3048 3638 3676 4152 5284 5779 5926 9426 9945 10873
11787 11837 1049 1218 1651 2328 3493 4363 5750 6483 7613
8782 9738 9803 11744 11937 1193 2060 2289 2964 3478 4592
4756 6709 7162 8231 8326 11140 11908 12243 978 2120 2439
3338 3850 4589 6567 8745 9656 9708 10161 10542 10711 12639
2403 2938 3117 3247 3711 5593 5844 5932 7801 10152 10226
11498 12162 12941 1781 2229 2276 2533 3582 3951 5279 5774
7930 9824 10920 11038 12340 12440 289 384 1980 2230 3464
3873 5958 8656 8942 9006 10175 11425 11745 12530 155 354
1090 1330 2002 2236 3559 3705 4922 5958 6576 8564 9972
12760 303 876 2059 2142 5244 5330 6644 7576 8614 9598
10410 10718 11033 12957 3449 3617 4408 4602 4727 6182 8835
8928 9372 9644 10237 10747 11655 12747 811 2565 2820 8677
8974 9632 11069 11548 11839 12107 12411 12695 12812 12890
972 4123 4943 6385 6449 7339 7477 8379 9177 9359 10074
11709 12552 12831 842 973 1541 2262 2905 5276 6758 7099
7894 8128 8325 8663 8875 10050 474 791 968 3902 4924 4965
5085 5908 6109 6329 7931 9038 9401 10568 1397 4461 4658
5911 6037 7127 7318 8678 8924 9000 9473 9602 10446 12692
1334 7571 12881
1393 1447 7972
633 1257 10597
4843 5102 11056
3294 8015 10513
1108 10374 10546
5353 7824 10111
3398 7674 8569
7719 9478 10503
2997 9418 9581
5777 6519 11229
1966 5214 9899
6 4088 5827
836 9248 9612
483 7229 7548
7865 8289 9804
2915 11098 11900
6180 7096 9481
1431 6786 8924
748 6757 8625
3312 4475 7204
1852 8958 11020
1915 2903 4006
6776 10886 12531
2594 9998 12742
159 2002 12079
853 3281 3762
5201 5798 6413
3882 6062 12047
4133 6775 9657
228 6874 11183
7433 10728 10864
7735 8073 12734
2844 4621 11779
3909 7103 12804
6002 9704 11060
5864 6856 7681
3652 5869 7605
2546 2657 4461
2423 4203 9111
244 1855 4691
1106 2178 6371
391 1617 10126
250 9259 10603
3435 4614 6924
1742 8045 9529
7667 8875 11451
4023 6108 6911
8621 10184 11650
6726 10861 12348
3228 6302 7388
1 1137 5358
381 2424 8537
3256 7508 10044
1980 2219 4569
2468 5699 10319
2803 3314 12808
8578 9642 11533
829 4585 7923
59 329 5575
1067 5709 6867
1175 4744 12219
109 2518 6756
2105 10626 11153
5192 10696 10749
6260 7641 8233
2998 3094 11214
3398 6466 11494
6574 10448 12160
2734 10755 12780
1028 7958 10825
8545 8602 10793
392 3398 11417
6639 9291 12571
1067 7919 8934
1064 2848 12753
6076 8656 12690
5504 6193 10171
1951 7156 7356
4389 4780 7889
526 4804 9141
1238 3648 10464
2587 5624 12557
5560 5903 11963
1134 2570 3297
10041 11583 12157
1263 9585 12912
3744 7898 10646
45 9074 10315
1051 6188 10038
2242 8394 12712
3598 9025 12651
2295 3540 5610
1914 4378 12423
1766 3635 12759
5177 9586 11143
943 3590 11649
4864 6905 10454
5852 6042 10421
6095 8285 12349
2070 7171 8563
718 12234 12716
512 10667 11353
3629 6485 7040
2880 8865 11466
4490 10220 11796
5440 8819 9103
5262 7543 12411
516 7779 10940
2515 5843 9202
4684 5994 10586
573 2270 3324
7870 8317 10322
6856 7638 12909
1583 7669 10781
8141 9085 12555
3903 5485 9992
4467 11998 12904.
16. A receiving method comprising:
receiving at least one transmission stream including symbols representative of constellation values;
demodulating the symbols into cell words associated with Low Density Parity Check (LDPC) codewords; wherein
each of the symbols is associated with a point of a NUC, Non-Uniform Constellation,
the NUC includes sixty-four points;
the NUC includes complex points defined by their real and imaginary parts as:
1.4480+j0.2403
0.6406+j1.1995
1.0952+j0.9115
0.6868+j0.8108
1.0500+j0.1642
0.7170+j0.1473
1.0519+j0.5188
0.7146+j0.4532
0.1677+j1.0405
0.2402+j1.4087
0.1369+j0.7073
0.4044+j0.7057
0.1374+j0.1295
0.4185+j0.1357
0.1325+j0.3998
0.4122+j0.4120;
and wherein a code rate of the LDPC is 12/15.
17. The receiving method according to claim 16 , wherein a first quarter of the NUC includes complex points defined by their real and imaginary parts as:
1.4480+j0.2403
0.6406+j1.1995
1.0952+j0.9115
0.6868+j0.8108
1.0500+j0.1642
0.7170+j0.1473
1.0519+j0.5188
0.7146+j0.4532
0.1677+j1.0405
0.2402+j1.4087
0.1369+j0.7073
0.4044+j0.7057
0.1374+j0.1295
0.4185+j0.1357
0.1325+j0.3998
0.4122+j0.4120;
a second quarter of the NUC includes points, each being an opposite of a complex conjugate of a point of the first quarter;
a third quarter of the NUC includes points, each being a complex conjugate of a point of the first quarter; and
a fourth quarter of the NUC includes points, each being an opposite of a point of the first quarter.
18. The receiving method according to claim 16 , wherein the at least one transmission stream is a digital video broadcasting stream.
19. The receiving method according to claim 16 , further comprising decoding the cell words into output data.
20. The receiving method according to claim 16 , wherein
the LDPC has a code length of 64800 bits and is associated with a parity check matrix initial value table showing positions of elements corresponding to the value “1” in an information matrix portion in units of 360 columns and
wherein the parity check matrix initial value table includes:
584 1472 1621 1867 3338 3568 3723 4185 5126 5889 7737 8632
8940 9725 221 445 590 3779 3835 6939 7743 8280 8448 8491 9367
10042 11242 12917 4662 4837 4900 5029 6449 6687 6751 8684 9936
11681 11811 11886 12089 12909 2418 3018 3647 4210 4473 7447
7502 9490 10067 11092 11139 11256 12201 12383 2591 2947 3349
3406 4417 4519 5176 6672 8498 8863 9201 11294 11376 12184
27 101 197 290 871 1727 3911 5411 6676 8701 9350 10310 10798
12439 1765 1897 2923 3584 3901 4048 6963 7054 7132 9165 10184
10824 11278 12669 2183 3740 4808 5217 5660 6375 6787 8219 8466
9037 10353 10583 11118 12762 73 1594 2146 2715 3501 3572 3639
3725 6959 7187 8406 10120 10507 10691 240 732 1215 2185 2788
2830 3499 3881 4197 4991 6425 7061 9756 10491 831 1568 1828
3424 4319 4516 4639 6018 9702 10203 10417 11240 11518 12458
2024 2970 3048 3638 3676 4152 5284 5779 5926 9426 9945 10873
11787 11837 1049 1218 1651 2328 3493 4363 5750 6483 7613 8782
9738 9803 11744 11937 1193 2060 2289 2964 3478 4592 4756 6709
7162 8231 8326 11140 11908 12243 978 2120 2439 3338 3850 4589
6567 8745 9656 9708 10161 10542 10711 12639 2403 2938 3117
3247 3711 5593 5844 5932 7801 10152 10226 11498 12162 12941
1781 2229 2276 2533 3582 3951 5279 5774 7930 9824 10920 11038
12340 12440 289 384 1980 2230 3464 3873 5958 8656 8942 9006
10175 11425 11745 12530 155 354 1090 1330 2002 2236 3559 3705
4922 5958 6576 8564 9972 12760 303 876 2059 2142 5244 5330
6644 7576 8614 9598 10410 10718 11033 12957 3449 3617 4408
4602 4727 6182 8835 8928 9372 9644 10237 10747 11655 12747
811 2565 2820 8677 8974 9632 11069 11548 11839 12107 12411
12695 12812 12890 972 4123 4943 6385 6449 7339 7477 8379 9177
9359 10074 11709 12552 12831 842 973 1541 2262 2905 5276 6758
7099 7894 8128 8325 8663 8875 10050 474 791 968 3902 4924 4965
5085 5908 6109 6329 7931 9038 9401 10568 1397 4461 4658 5911
6037 7127 7318 8678 8924 9000 9473 9602 10446 12692
1334 7571 12881
1393 1447 7972
633 1257 10597
4843 5102 11056
3294 8015 10513
1108 10374 10546
5353 7824 10111
3398 7674 8569
7719 9478 10503
2997 9418 9581
5777 6519 11229
1966 5214 9899
6 4088 5827
836 9248 9612
483 7229 7548
7865 8289 9804
2915 11098 11900
6180 7096 9481
1431 6786 8924
748 6757 8625
3312 4475 7204
1852 8958 11020
1915 2903 4006
6776 10886 12531
2594 9998 12742
159 2002 12079
853 3281 3762
5201 5798 6413
3882 6062 12047
4133 6775 9657
228 6874 11183
7433 10728 10864
7735 8073 12734
2844 4621 11779
3909 7103 12804
6002 9704 11060
5864 6856 7681
3652 5869 7605
2546 2657 4461
2423 4203 9111
244 1855 4691
1106 2178 6371
391 1617 10126
250 9259 10603
3435 4614 6924
1742 8045 9529
7667 8875 11451
4023 6108 6911
8621 10184 11650
6726 10861 12348
3228 6302 7388
1 1137 5358
381 2424 8537
3256 7508 10044
1980 2219 4569
2468 5699 10319
2803 3314 12808
8578 9642 11533
829 4585 7923
59 329 5575
1067 5709 6867
1175 4744 12219
109 2518 6756
2105 10626 11153
5192 10696 10749
6260 7641 8233
2998 3094 11214
3398 6466 11494
6574 10448 12160
2734 10755 12780
1028 7958 10825
8545 8602 10793
392 3398 11417
6639 9291 12571
1067 7919 8934
1064 2848 12753
6076 8656 12690
5504 6193 10171
1951 7156 7356
4389 4780 7889
526 4804 9141
1238 3648 10464
2587 5624 12557
5560 5903 11963
1134 2570 3297
10041 11583 12157
1263 9585 12912
3744 7898 10646
45 9074 10315
1051 6188 10038
2242 8394 12712
3598 9025 12651
2295 3540 5610
1914 4378 12423
1766 3635 12759
5177 9586 11143
943 3590 11649
4864 6905 10454
5852 6042 10421
6095 8285 12349
2070 7171 8563
718 12234 12716
512 10667 11353
3629 6485 7040
2880 8865 11466
4490 10220 11796
5440 8819 9103
5262 7543 12411
516 7779 10940
2515 5843 9202
4684 5994 10586
573 2270 3324
7870 8317 10322
6856 7638 12909
1583 7669 10781
8141 9085 12555
3903 5485 9992
4467 11998 12904.