Point Forecast Matrices
Issued by NWS Dallas/Fort Worth, TX

Home |  Current Version |  Previous Version |  Graphics & Text |  Print | Product List |  Glossary Off
Versions: 1 2 3 4 5 6 7 8 9
438
FOUS54 KFWD 141011
PFMFWD

Point Forecast Matrices
National Weather Service Fort Worth TX
509 AM CDT Sun Jul 14 2024

TXZ118-142100-
DFW Airport-Dallas TX
32.91N  97.03W Elev. 562 ft
509 AM CDT Sun Jul 14 2024

Date             Sun 07/14/24            Mon 07/15/24            Tue 07/16/24
CDT 3hrly     04 07 10 13 16 19 22 01 04 07 10 13 16 19 22 01 04 07 10 13 16 19
UTC 3hrly     09 12 15 18 21 00 03 06 09 12 15 18 21 00 03 06 09 12 15 18 21 00

Max/Min                      98          80         100          81         100
Temp             77 86 94 97 96 89 85 82 80 88 97100 98 90 87 83 81 89 97100 98
Dewpt            70 72 69 67 67 68 70 70 71 71 67 65 64 66 69 70 70 69 68 64 63
RH               79 63 44 38 39 50 61 67 74 57 38 32 33 45 55 65 69 52 39 31 32
Wind dir          S SW SW  S  S  S  S  S SW SW  S  S  S  S  S  S  S  S  S  S  S
Wind spd         10 10  9 10 12 12 12 11 10 11 10 13 13 13 13 12 11 11 10 12 12
Clouds           CL FW FW FW FW FW CL FW FW FW FW FW FW FW CL FW FW FW FW FW FW
PoP 12hr                      0           0           0           0           0
QPF 12hr                      0           0           0           0           0
Snow 12hr                 00-00       00-00       00-00
Heat index          92 99101100 93 90 86 83 94101104101 93 91 87 85 94102103100
Max heat               99   103    98    88   101   104    98    90   102   103


Date          Wed 07/17/24  Thu 07/18/24  Fri 07/19/24  Sat 07/20/24
CDT 6hrly     01 07 13 19   01 07 13 19   01 07 13 19   01 07 13 19
UTC 6hrly     06 12 18 00   06 12 18 00   06 12 18 00   06 12 18 00

Min/Max          81   101      80    93      74    90      73    92
Temp          86 81 97 97   85 80 90 89   79 74 87 88   78 73 88 89
Dewpt         68 71 70 65   70 71 72 69   70 70 68 63   67 67 66 63
PWind dir         S     S       S     N      NE    NE       E     E
Wind char        GN    GN      GN    LT      LT    GN      LT    LT
Avg clouds    FW FW FW FW   SC B1 B1 B1   B1 SC SC SC   SC SC SC SC
PoP 12hr          0     5      20    40      30    30      20    30
Rain shwrs                      S  S  C    S  C  C  C       S  S  C
Tstms                           S  S  C    S  S     S             S

$$
TXZ159-142100-
Waco Airport-McLennan TX
31.62N  97.22W Elev. 516 ft
509 AM CDT Sun Jul 14 2024

Date             Sun 07/14/24            Mon 07/15/24            Tue 07/16/24
CDT 3hrly     04 07 10 13 16 19 22 01 04 07 10 13 16 19 22 01 04 07 10 13 16 19
UTC 3hrly     09 12 15 18 21 00 03 06 09 12 15 18 21 00 03 06 09 12 15 18 21 00

Max/Min                      98          76         100          76          99
Temp             75 84 94 98 93 83 80 78 76 87 96100 96 86 83 79 76 85 95 99 95
Dewpt            71 73 70 68 67 69 71 73 73 72 69 65 67 69 72 71 70 71 68 64 64
RH               87 70 46 38 43 63 74 85 90 61 42 32 39 57 70 77 82 63 42 32 36
Wind dir          S SW  S  S  S  S  S  S  S  S  S  S  S  S  S  S  S  S  S  S  S
Wind spd          5  5  6  9 10  9  8  6  5  6  9 10 10 10  9  9  6  9  9 10 10
Clouds           FW CL CL FW FW CL CL CL CL CL CL FW FW CL CL CL CL CL CL FW FW
PoP 12hr                      0           5           0           0           0
QPF 12hr                      0           0           0           0           0
Snow 12hr                 00-00       00-00       00-00
Heat index          90100104 97 87 83       94102104100 90 88       90100102 97
Max heat              100   104    94    84   102   104    97    86   100   102


Date          Wed 07/17/24  Thu 07/18/24  Fri 07/19/24  Sat 07/20/24
CDT 6hrly     01 07 13 19   01 07 13 19   01 07 13 19   01 07 13 19
UTC 6hrly     06 12 18 00   06 12 18 00   06 12 18 00   06 12 18 00

Min/Max          77    99      76    96      73    91      71    91
Temp          82 77 95 95   80 77 93 91   79 73 88 87   75 71 88 89
Dewpt         72 73 70 67   73 72 72 70   73 72 72 68   70 69 69 66
PWind dir         S     S       S    NW      NE    NE       E     E
Wind char        GN    LT      LT    LT      LT    LT      LT    LT
Avg clouds    CL CL FW FW   FW SC SC B1   B1 B1 SC SC   SC SC SC SC
PoP 12hr          0     5       5    20      30    40      20    30
Rain shwrs                            S    S  C  C  C       S  C  C
Tstms                                 S    S  C  S  S             S

$$
TXZ146-142100-
Corsicana-Navarro TX
32.03N  96.39W Elev. 449 ft
509 AM CDT Sun Jul 14 2024

Date             Sun 07/14/24            Mon 07/15/24            Tue 07/16/24
CDT 3hrly     04 07 10 13 16 19 22 01 04 07 10 13 16 19 22 01 04 07 10 13 16 19
UTC 3hrly     09 12 15 18 21 00 03 06 09 12 15 18 21 00 03 06 09 12 15 18 21 00

Max/Min                      97          76          99          78          98
Temp             72 83 92 97 92 84 80 79 77 88 96 99 94 86 82 79 78 87 95 97 94
Dewpt            72 74 72 70 69 72 72 73 73 73 70 68 68 71 72 72 72 71 70 67 67
RH              100 74 52 42 47 67 77 82 87 61 43 37 43 61 72 79 82 59 45 38 41
Wind dir          S SW SW  S  S  S  S  S  S SW  S  S  S  S  S  S  S  S  S  S  S
Wind spd          6  8  8 10 10 10  9  9  8 10 10 11 11 10 10 10  9 10 10 11 11
Clouds           FW FW CL CL FW CL CL CL FW FW FW FW FW CL CL CL CL CL CL CL FW
PoP 12hr                      5           5           0           0           0
QPF 12hr                      0           0           0           0           0
Snow 12hr                 00-00       00-00       00-00
Heat index          90100104 97 90 84       96103105 99 91 87       93102101 98
Max heat              100   104    94    84   103   105    96    85   102   102


Date          Wed 07/17/24  Thu 07/18/24  Fri 07/19/24  Sat 07/20/24
CDT 6hrly     01 07 13 19   01 07 13 19   01 07 13 19   01 07 13 19
UTC 6hrly     06 12 18 00   06 12 18 00   06 12 18 00   06 12 18 00

Min/Max          78    99      77    95      73    90      72    91
Temp          83 78 95 95   81 77 92 90   78 73 87 87   77 72 88 88
Dewpt         72 73 70 68   72 73 71 70   72 71 70 67   70 69 68 66
PWind dir         S     S       S    NW      NE    NE       E     E
Wind char        GN    GN      GN    LT      LT    LT      LT    LT
Avg clouds    CL CL FW FW   FW SC SC B1   B1 B1 B1 SC   SC SC SC SC
PoP 12hr          0     5      10    30      40    40      20    30
Rain shwrs                            C    C  C  C  C       S  C  C
Tstms                                 C    C  C  S  C             S

$$
TXZ119-142100-
Dallas Love Field-Dallas TX
32.86N  96.85W Elev. 487 ft
509 AM CDT Sun Jul 14 2024

Date             Sun 07/14/24            Mon 07/15/24            Tue 07/16/24
CDT 3hrly     04 07 10 13 16 19 22 01 04 07 10 13 16 19 22 01 04 07 10 13 16 19
UTC 3hrly     09 12 15 18 21 00 03 06 09 12 15 18 21 00 03 06 09 12 15 18 21 00

Max/Min                     100          80         102          81         101
Temp             77 87 95 99 97 89 85 81 80 89 98102 99 90 85 82 81 89 97101 98
Dewpt            71 72 69 67 66 68 70 71 71 71 67 64 67 69 71 71 71 71 69 65 64
RH               82 61 43 36 36 50 61 72 74 56 37 29 36 50 63 69 72 56 40 31 33
Wind dir          S SW SW  S  S  S  S  S  S SW  S  S  S  S  S  S  S  S  S  S  S
Wind spd          5  6  6  8 10  9  9  6  6  8  8 10 10 10 10  9  8  8  8 10 10
Clouds           CL FW FW FW FW FW FW FW FW FW FW FW FW FW FW FW FW FW FW FW FW
PoP 12hr                      0           5           0           0           0
QPF 12hr                      0           0           0           0           0
Snow 12hr                 00-00       00-00       00-00
Heat index          94101104101 93 90 85 83 95103105104 95 90 86 85 95103105101
Max heat              101   105    99    88   103   105   101    89   103   105


Date          Wed 07/17/24  Thu 07/18/24  Fri 07/19/24  Sat 07/20/24
CDT 6hrly     01 07 13 19   01 07 13 19   01 07 13 19   01 07 13 19
UTC 6hrly     06 12 18 00   06 12 18 00   06 12 18 00   06 12 18 00

Min/Max          81   102      80    94      74    91      73    92
Temp          86 81 97 98   84 80 91 90   79 74 88 88   77 73 88 89
Dewpt         70 72 71 67   71 72 73 71   72 70 69 65   68 68 68 65
PWind dir         S     S       S    NW      NE    NE       E     E
Wind char        GN    LT      LT    LT      LT    LT      LT    LT
Avg clouds    FW FW FW FW   SC B1 B1 B1   SC SC SC SC   SC SC SC SC
PoP 12hr          0     5      20    40      30    30      20    30
Rain shwrs                      S  S  C    S  C  C  C       S  S  C
Tstms                           S  S  C    S  S     S             S

$$
TXZ103-142100-
Denton-Denton TX
33.20N  97.17W Elev. 642 ft
509 AM CDT Sun Jul 14 2024

Date             Sun 07/14/24            Mon 07/15/24            Tue 07/16/24
CDT 3hrly     04 07 10 13 16 19 22 01 04 07 10 13 16 19 22 01 04 07 10 13 16 19
UTC 3hrly     09 12 15 18 21 00 03 06 09 12 15 18 21 00 03 06 09 12 15 18 21 00

Max/Min                      99          77         101          79         102
Temp             77 87 95 98 97 88 84 79 79 89 98101 99 90 85 81 80 89 97101 99
Dewpt            71 72 70 67 65 67 69 68 69 71 68 64 65 66 69 69 70 70 68 65 64
RH               82 61 45 37 35 50 61 69 72 56 38 30 33 45 59 67 72 54 39 31 32
Wind dir          S SW SW  S  S  S  S  S  S SW  S  S  S  S  S  S  S  S  S  S  S
Wind spd          8 10  9 10 10 10 10  9  9 10 10 12 12 11 10 10 10 10 10 11 11
Clouds           FW CL FW FW FW FW CL CL FW FW FW FW FW CL FW CL FW FW FW FW FW
PoP 12hr                      0           0           0           0           0
QPF 12hr                      0           0           0           0           0
Snow 12hr                 00-00       00-00       00-00
Heat index          94102103100 91 88       95104104102 93 89 84 83 94102105102
Max heat              102   104    98    85   104   105    99    87   102   105


Date          Wed 07/17/24  Thu 07/18/24  Fri 07/19/24  Sat 07/20/24
CDT 6hrly     01 07 13 19   01 07 13 19   01 07 13 19   01 07 13 19
UTC 6hrly     06 12 18 00   06 12 18 00   06 12 18 00   06 12 18 00

Min/Max          79   101      75    92      70    90      69    92
Temp          86 79 98 97   81 76 89 89   77 71 87 88   74 71 87 90
Dewpt         68 70 69 65   70 71 72 69   70 69 68 64   67 67 66 63
PWind dir         S     S       S     N      NE    NE       E     E
Wind char        GN    GN      LT    LT      LT    LT      LT    LT
Avg clouds    FW FW SC SC   SC B1 B1 B1   SC SC SC SC   FW SC SC SC
PoP 12hr          0     5      20    40      20    30      10    20
Rain shwrs                      S  C  C    S  S  C  C          S  S
Tstms                           S  C  C    S  S     S             S

$$
TXZ095-142100-
Paris-Lamar TX
33.64N  95.45W Elev. 530 ft
509 AM CDT Sun Jul 14 2024

Date             Sun 07/14/24            Mon 07/15/24            Tue 07/16/24
CDT 3hrly     04 07 10 13 16 19 22 01 04 07 10 13 16 19 22 01 04 07 10 13 16 19
UTC 3hrly     09 12 15 18 21 00 03 06 09 12 15 18 21 00 03 06 09 12 15 18 21 00

Max/Min                      96          76          97          77          96
Temp             72 83 92 94 92 82 80 78 76 87 94 97 94 82 81 78 77 87 93 96 93
Dewpt            71 71 72 70 71 70 72 71 71 73 71 69 71 71 72 72 74 73 72 71 70
RH               97 67 52 46 51 67 77 79 85 63 47 40 47 69 74 82 90 63 51 45 47
Wind dir          S SW SW  S  S  S  S  S  S SW SW  S  S  S  S  S  S SW  S  S  S
Wind spd          5  8  6  8  9  6  6  6  6  9 10 10 10  9  9  9  9 10 10 10  9
Clouds           SC FW FW SC SC FW FW FW SC FW FW FW FW FW FW FW FW FW FW FW CL
PoP 12hr                     10           5           0           0           0
QPF 12hr                      0           0           0           0           0
Snow 12hr                 00-00       00-00       00-00
Heat index          88100100 99 86 84       94101103101 86 85       94101104 99
Max heat              100   102    95         101   103    96    84   101   104


Date          Wed 07/17/24  Thu 07/18/24  Fri 07/19/24  Sat 07/20/24
CDT 6hrly     01 07 13 19   01 07 13 19   01 07 13 19   01 07 13 19
UTC 6hrly     06 12 18 00   06 12 18 00   06 12 18 00   06 12 18 00

Min/Max          77    97      75    87      70    85      68    88
Temp          80 77 94 94   80 75 85 84   74 70 82 83   71 68 84 86
Dewpt         71 73 73 70   73 73 74 71   71 69 68 67   68 66 67 66
PWind dir         S     S       S     N      NE    NE       E     E
Wind char        GN    LT      LT    LT      LT    LT      LT    LT
Avg clouds    FW FW FW FW   SC B2 B2 B1   B1 B1 SC SC   SC SC SC SC
PoP 12hr          0    10      30    50      30    30      10    20
Rain shwrs                   S  C  C  C    S  C  C  C          S  S
Tstms                        S  C  C  C    S  S  S  S

$$
TXZ121-142100-
Terrell-Kaufman TX
32.71N  96.27W Elev. 474 ft
509 AM CDT Sun Jul 14 2024

Date             Sun 07/14/24            Mon 07/15/24            Tue 07/16/24
CDT 3hrly     04 07 10 13 16 19 22 01 04 07 10 13 16 19 22 01 04 07 10 13 16 19
UTC 3hrly     09 12 15 18 21 00 03 06 09 12 15 18 21 00 03 06 09 12 15 18 21 00

Max/Min                      95          76          98          77          98
Temp             72 83 92 94 93 84 80 78 76 87 94 97 94 85 83 79 77 86 94 97 94
Dewpt            72 73 72 70 70 70 72 72 73 74 70 68 67 69 71 71 71 71 69 66 65
RH              100 72 52 46 47 63 77 82 90 65 46 39 41 59 67 77 82 61 44 36 39
Wind dir          S SW SW  S  S  S  S  S  S SW  S  S  S  S  S  S  S  S  S  S  S
Wind spd          5  8  8  9 10  9  8  8  8 10 10 11 11 10  9  9  9 10 10 10 10
Clouds           SC FW FW FW FW FW CL FW FW FW FW FW FW CL FW FW FW FW FW FW FW
PoP 12hr                      5           5           0           0           0
QPF 12hr                      0           0           0           0           0
Snow 12hr                 00-00       00-00       00-00
Heat index          89100100 99 88 84       95100102 98 89 88       91 99101 97
Max heat              100   102    96         100   103    95    86    99   101


Date          Wed 07/17/24  Thu 07/18/24  Fri 07/19/24  Sat 07/20/24
CDT 6hrly     01 07 13 19   01 07 13 19   01 07 13 19   01 07 13 19
UTC 6hrly     06 12 18 00   06 12 18 00   06 12 18 00   06 12 18 00

Min/Max          77    98      76    92      71    88      69    90
Temp          82 77 95 94   80 76 89 87   76 71 85 85   74 69 86 87
Dewpt         70 72 70 66   70 72 71 69   70 69 67 64   67 66 66 63
PWind dir         S     S       S     N      NE    NE       E     E
Wind char        GN    GN      LT    LT      LT    LT      LT    LT
Avg clouds    CL CL FW FW   SC SC B1 B1   SC SC B1 SC   SC SC SC SC
PoP 12hr          0     5      20    40      40    30      20    30
Rain shwrs                      S  S  C    S  C  C  C       S  S  C
Tstms                           S  S  C    S  C  S  S             S

$$
TXZ104-142100-
McKinney-Collin TX
33.18N  96.59W Elev. 585 ft
509 AM CDT Sun Jul 14 2024

Date             Sun 07/14/24            Mon 07/15/24            Tue 07/16/24
CDT 3hrly     04 07 10 13 16 19 22 01 04 07 10 13 16 19 22 01 04 07 10 13 16 19
UTC 3hrly     09 12 15 18 21 00 03 06 09 12 15 18 21 00 03 06 09 12 15 18 21 00

Max/Min                      98          78         100          79         100
Temp             74 86 94 98 96 87 83 80 78 89 97100 98 88 84 81 79 89 97 99 97
Dewpt            71 72 70 68 69 70 71 70 71 71 67 65 66 69 70 70 71 70 69 66 65
RH               90 63 46 38 42 57 67 72 79 56 38 32 35 54 63 69 77 54 40 34 35
Wind dir          S SW SW  S  S  S  S  S  S SW  S  S  S  S  S  S  S  S  S  S  S
Wind spd          6  9  9 10 10 10 10  9  9 10 10 12 12 11 10 10 10 10 11 12 11
Clouds           FW CL FW FW FW SC FW FW FW FW FW FW FW CL FW FW FW FW FW FW FW
PoP 12hr                      0           5           0           0           0
QPF 12hr                      0           0           0           0           0
Snow 12hr                 00-00       00-00       00-00
Heat index          92100104102 92 88 83    95101104102 92 88 85    94103103100
Max heat              100   104    97    85   101   104    98    87   103   103


Date          Wed 07/17/24  Thu 07/18/24  Fri 07/19/24  Sat 07/20/24
CDT 6hrly     01 07 13 19   01 07 13 19   01 07 13 19   01 07 13 19
UTC 6hrly     06 12 18 00   06 12 18 00   06 12 18 00   06 12 18 00

Min/Max          79   100      77    92      72    90      70    91
Temp          84 79 97 96   82 77 89 87   77 72 87 87   74 70 88 89
Dewpt         70 71 70 65   71 72 72 68   70 69 67 63   67 66 66 63
PWind dir         S     S       S     N      NE    NE       E     E
Wind char        GN    GN      LT    LT      LT    LT      LT    LT
Avg clouds    FW FW FW FW   SC B1 B1 B1   SC SC SC SC   SC SC SC SC
PoP 12hr          0     5      20    40      30    30      10    20
Rain shwrs                      S  C  C    S  C  C  C          S  S
Tstms                           S  C  C    S  S     S             S

$$
TXZ158-142100-
Temple-Bell TX
31.15N  97.42W Elev. 682 ft
509 AM CDT Sun Jul 14 2024

Date             Sun 07/14/24            Mon 07/15/24            Tue 07/16/24
CDT 3hrly     04 07 10 13 16 19 22 01 04 07 10 13 16 19 22 01 04 07 10 13 16 19
UTC 3hrly     09 12 15 18 21 00 03 06 09 12 15 18 21 00 03 06 09 12 15 18 21 00

Max/Min                      95          74          98          74          99
Temp             73 85 91 94 92 83 80 76 74 87 95 97 94 85 81 76 74 86 95 98 95
Dewpt            72 73 71 69 68 70 71 73 72 72 68 65 67 69 71 70 70 71 66 65 64
RH               97 67 52 44 46 65 74 90 93 61 42 35 41 59 72 82 87 61 39 34 36
Wind dir          S SW  S  S  S  S  S  S  S  S  S  S  S  S  S  S  S  S  S  S  S
Wind spd          5  8  9 10 12 10  9  9  6  9 10 12 13 10 10 10  9 10 11 12 12
Clouds           SC FW FW FW FW FW FW FW FW CL CL CL CL CL CL FW FW FW CL CL FW
PoP 12hr                      0           0           0           0           0
QPF 12hr                      0           0           0           0           0
Snow 12hr                 00-00       00-00       00-00
Heat index          92 98 99 96 87 83       94100100 98 89 85       91 98101 97
Max heat               98   101    95         100   100    95    82    98   101


Date          Wed 07/17/24  Thu 07/18/24  Fri 07/19/24  Sat 07/20/24
CDT 6hrly     01 07 13 19   01 07 13 19   01 07 13 19   01 07 13 19
UTC 6hrly     06 12 18 00   06 12 18 00   06 12 18 00   06 12 18 00

Min/Max          76    98      75    96      72    90      70    93
Temp          82 76 95 94   80 76 92 91   79 72 87 87   76 71 89 89
Dewpt         72 73 70 68   73 72 71 69   72 72 71 68   70 69 68 66
PWind dir         S     S       S    NW      NE    NE       E     E
Wind char        GN    GN      GN    LT      LT    LT      LT    LT
Avg clouds    FW FW FW FW   FW SC SC SC   B1 B1 B1 SC   SC SC SC SC
PoP 12hr          0     5       5    20      30    40      20    30
Rain shwrs                            S    S  C  C  C       S  C  C
Tstms                                 S    S  C  S  C             S

$$
TXZ116-142100-
Mineral Wells-Palo Pinto TX
32.79N  98.07W Elev. 972 ft
509 AM CDT Sun Jul 14 2024

Date             Sun 07/14/24            Mon 07/15/24            Tue 07/16/24
CDT 3hrly     04 07 10 13 16 19 22 01 04 07 10 13 16 19 22 01 04 07 10 13 16 19
UTC 3hrly     09 12 15 18 21 00 03 06 09 12 15 18 21 00 03 06 09 12 15 18 21 00

Max/Min                      99          74         101          77         102
Temp             72 85 94 97 96 86 81 77 75 88 98101 99 87 83 79 77 89 98101 99
Dewpt            69 72 69 65 64 65 66 66 68 70 65 63 63 65 65 65 66 68 65 61 60
RH               90 65 44 35 35 50 60 69 79 55 34 29 31 48 55 62 69 50 34 27 28
Wind dir          S SW SW  S  S  S  S  S  S SW  S  S  S  S  S  S  S SW  S  S  S
Wind spd          6 10  9 10 10 10 10  9  8 10 10 11 11 10 10 10  9 10 10 10 10
Clouds           CL CL FW FW CL CL CL CL CL CL CL FW CL CL CL CL CL CL CL FW FW
PoP 12hr                      0           0           0           0           0
QPF 12hr                      0           0           0           0           0
Snow 12hr                 00-00       00-00       00-00
Heat index          91 99100 98 88 83       93101103101 89 85       93101102 99
Max heat               99   101    96         101   103    97    83   101   102


Date          Wed 07/17/24  Thu 07/18/24  Fri 07/19/24  Sat 07/20/24
CDT 6hrly     01 07 13 19   01 07 13 19   01 07 13 19   01 07 13 19
UTC 6hrly     06 12 18 00   06 12 18 00   06 12 18 00   06 12 18 00

Min/Max          77   100      75    92      70    91      68    93
Temp          84 77 97 94   79 75 89 90   75 70 88 89   74 68 89 89
Dewpt         65 68 66 64   68 69 69 68   69 68 66 62   65 65 64 62
PWind dir         S     S       S     N      NE    NE       E     E
Wind char        GN    LT      LT    LT      LT    LT      LT    LT
Avg clouds    FW FW FW SC   SC B1 B1 B1   SC SC SC SC   FW SC SC SC
PoP 12hr          0     5      10    30      20    30      10    20
Rain shwrs                         S  C       S  C  C          S  S
Tstms                              S  C       S     S             S

$$