Point Forecast Matrices
Issued by NWS Cleveland, OH
Issued by NWS Cleveland, OH
899 FOUS51 KCLE 261743 PFMCLE Point Forecast Matrices National Weather Service CLEVELAND, OHIO 142 PM EDT Sun May 26 2024 PAZ001-270800- ERIE-ERIE PA 42.08N 80.18W Elev. 733 ft 142 PM EDT Sun May 26 2024 Date 05/26/24 Mon 05/27/24 Tue 05/28/24 Wed EDT 3hrly 17 20 23 02 05 08 11 14 17 20 23 02 05 08 11 14 17 20 23 02 05 08 UTC 3hrly 21 00 03 06 09 12 15 18 21 00 03 06 09 12 15 18 21 00 03 06 09 12 Min/Max 65 76 59 71 55 Temp 75 74 69 68 65 67 71 76 73 68 62 60 59 62 66 68 70 66 61 58 56 58 Dewpt 57 58 61 61 61 62 63 63 61 57 56 54 54 54 55 54 53 52 53 52 50 50 RH 54 57 76 78 87 84 76 64 66 68 81 81 83 75 68 61 55 61 75 80 80 75 Wind dir NE E SE S S S S SW SW W W W W SW W W W W W W W NW Wind spd 12 10 13 14 14 16 17 14 13 17 17 16 14 13 14 17 13 9 8 6 9 10 Clouds B1 B2 OV B2 B2 OV OV B2 B2 B1 B1 SC SC SC B1 SC SC B1 B1 B1 B1 B2 PoP 12hr 90 80 20 60 50 QPF 12hr 0.36 0.28 0.02 0.06 0.05 Snow 12hr 00-00 00-00 00-00 Rain shwrs S D C C D L C C S S C C L L C C C C C Tstms S D C C D L C C S S S C C S C S S Date 05/29 Thu 05/30/24 Fri 05/31/24 Sat 06/01/24 Sun 06/02/24 EDT 6hrly 14 20 02 08 14 20 02 08 14 20 02 08 14 20 02 08 14 20 UTC 6hrly 18 00 06 12 18 00 06 12 18 00 06 12 18 00 06 12 18 00 Max/Min 65 50 66 51 71 54 77 61 77 Temp 61 59 52 54 63 62 53 55 66 66 57 59 73 71 61 65 73 72 Dewpt 48 43 40 43 42 40 41 44 44 46 46 48 50 52 51 54 56 56 PWind dir NW NW NW NW W SW W SE S Wind char GN GN GN LT LT LT LT LT GN Avg clouds B2 SC FW FW FW FW FW FW FW FW FW FW SC SC SC B1 B1 SC PoP 12hr 50 5 5 0 0 5 10 20 40 Rain shwrs C C S S C C Tstms S C S S C $$ OHZ033-270800- YOUNGSTOWN/WARREN-TRUMBULL OH 41.25N 80.67W Elev. 1196 ft 142 PM EDT Sun May 26 2024 Date 05/26/24 Mon 05/27/24 Tue 05/28/24 Wed EDT 3hrly 17 20 23 02 05 08 11 14 17 20 23 02 05 08 11 14 17 20 23 02 05 08 UTC 3hrly 21 00 03 06 09 12 15 18 21 00 03 06 09 12 15 18 21 00 03 06 09 12 Min/Max 64 77 57 71 53 Temp 80 74 68 66 65 67 71 76 76 70 61 58 57 61 66 69 70 66 59 55 54 56 Dewpt 62 63 62 62 62 63 64 64 62 57 54 53 53 54 55 54 52 52 51 51 50 51 RH 54 69 81 87 90 87 79 66 62 63 78 83 86 78 68 59 53 61 75 86 86 83 Wind dir SE SE SE S S S S SW SW W W W SW SW W W W W W W W W Wind spd 11 10 10 11 10 13 13 13 13 12 11 10 9 9 10 11 10 5 5 5 5 6 Wind gust 24 24 Clouds B2 OV OV B2 OV OV OV B2 B2 B1 B1 SC SC SC SC SC SC SC SC B1 B1 B1 PoP 12hr 90 80 20 70 60 QPF 12hr 0.28 0.18 0.01 0.09 0.03 Snow 12hr 00-00 00-00 00-00 Rain shwrs D L C D D L C C S S L L L L C C L L L Tstms D L C D D L C C S S C C C S C S S Heat index 81 Max heat 81 Date 05/29 Thu 05/30/24 Fri 05/31/24 Sat 06/01/24 Sun 06/02/24 EDT 6hrly 14 20 02 08 14 20 02 08 14 20 02 08 14 20 02 08 14 20 UTC 6hrly 18 00 06 12 18 00 06 12 18 00 06 12 18 00 06 12 18 00 Max/Min 64 44 67 44 72 48 78 57 77 Temp 61 58 47 50 65 61 47 51 70 66 51 55 75 72 59 61 75 72 Dewpt 48 43 39 41 39 40 38 42 42 45 42 46 48 51 50 54 57 58 PWind dir NW NW NW NW NW S S SE S Wind char GN LT GN LT LT LT LT LT LT Avg clouds B1 SC FW FW FW FW CL CL FW FW FW FW SC SC SC B1 B1 B1 PoP 12hr 70 5 0 0 0 5 10 30 40 Rain shwrs L C S C C C Tstms S C S S S C $$ OHZ032-270800- AKRON/CANTON-SUMMIT OH 40.92N 81.44W Elev. 1228 ft 142 PM EDT Sun May 26 2024 Date 05/26/24 Mon 05/27/24 Tue 05/28/24 Wed EDT 3hrly 17 20 23 02 05 08 11 14 17 20 23 02 05 08 11 14 17 20 23 02 05 08 UTC 3hrly 21 00 03 06 09 12 15 18 21 00 03 06 09 12 15 18 21 00 03 06 09 12 Min/Max 64 76 56 70 54 Temp 81 73 68 66 65 66 70 74 75 68 61 58 56 60 66 69 70 66 59 56 54 56 Dewpt 62 63 63 62 63 64 64 65 61 57 54 54 54 55 56 54 54 53 52 52 51 52 RH 53 71 84 87 93 93 81 74 62 68 78 86 93 84 70 59 57 63 78 86 90 86 Wind dir SE S S S S S SW SW W W W W SW SW W W W W W W W W Wind spd 12 13 11 12 12 13 14 16 17 14 12 9 8 9 11 12 12 6 5 6 6 9 Wind gust 26 27 25 Clouds B2 OV OV OV OV OV B2 B2 B1 B1 SC SC SC SC SC SC SC SC B1 B1 B1 B1 PoP 12hr 90 70 20 70 60 QPF 12hr 0.18 0.06 0 0.09 0.02 Snow 12hr 00-00 00-00 00-00 Rain shwrs S D C L D L C C S C C L L C C L L L Tstms S D C L D L C C S S C C C S C S Heat index 82 Max heat 83 Date 05/29 Thu 05/30/24 Fri 05/31/24 Sat 06/01/24 Sun 06/02/24 EDT 6hrly 14 20 02 08 14 20 02 08 14 20 02 08 14 20 02 08 14 20 UTC 6hrly 18 00 06 12 18 00 06 12 18 00 06 12 18 00 06 12 18 00 Max/Min 65 44 67 44 72 49 78 58 76 Temp 62 59 47 50 65 62 47 50 70 68 52 55 75 73 60 61 75 73 Dewpt 50 44 39 43 41 41 39 43 44 46 43 47 49 53 51 56 60 60 PWind dir NW NW NW N N E S S S Wind char GN LT LT LT LT LT LT LT LT Avg clouds B1 SC FW FW FW CL CL CL FW FW FW FW SC SC SC B1 B1 B1 PoP 12hr 60 5 0 0 0 10 20 30 40 Rain shwrs L C S S C C C Tstms S C S S S C $$ OHZ031-270800- WOOSTER-WAYNE OH 40.87N 81.89W Elev. 1136 ft 142 PM EDT Sun May 26 2024 Date 05/26/24 Mon 05/27/24 Tue 05/28/24 Wed EDT 3hrly 17 20 23 02 05 08 11 14 17 20 23 02 05 08 11 14 17 20 23 02 05 08 UTC 3hrly 21 00 03 06 09 12 15 18 21 00 03 06 09 12 15 18 21 00 03 06 09 12 Min/Max 64 76 56 73 54 Temp 82 73 68 66 65 66 72 75 75 68 60 58 56 61 68 70 72 68 60 56 54 56 Dewpt 62 63 63 63 63 64 65 64 61 57 54 53 53 56 56 55 54 54 52 52 51 52 RH 51 71 84 90 93 93 79 69 62 68 81 83 90 84 65 59 53 61 75 86 90 86 Wind dir SE S S S S S SW SW W W W W SW SW W W W W W W W W Wind spd 13 13 11 12 13 14 16 17 18 14 12 9 8 10 11 13 12 8 5 6 8 10 Wind gust 27 28 Clouds OV OV B2 OV OV OV B2 B2 B1 B1 SC SC SC SC SC SC SC SC SC B1 B1 SC PoP 12hr 90 70 10 60 60 QPF 12hr 0.23 0.07 0 0.07 0.03 Snow 12hr 00-00 00-00 00-00 Rain shwrs C D C L D L C S S C C L L L L L L L Tstms C D C L D L C S S S C C C S C S Heat index 82 Max heat 83 Date 05/29 Thu 05/30/24 Fri 05/31/24 Sat 06/01/24 Sun 06/02/24 EDT 6hrly 14 20 02 08 14 20 02 08 14 20 02 08 14 20 02 08 14 20 UTC 6hrly 18 00 06 12 18 00 06 12 18 00 06 12 18 00 06 12 18 00 Max/Min 66 44 68 45 73 49 79 59 78 Temp 64 60 47 50 66 63 49 52 71 69 53 56 76 73 61 62 77 74 Dewpt 50 45 40 44 42 42 41 44 45 48 44 47 51 54 53 57 60 60 PWind dir NW NW NW N N SE S SE S Wind char GN LT GN LT LT LT LT LT GN Avg clouds B1 SC FW FW CL CL CL CL CL FW FW FW SC SC SC B1 B1 B1 PoP 12hr 60 5 0 0 0 10 20 30 40 Rain shwrs L C S C C C C Tstms S C C S S C $$ OHZ011-270800- CLEVELAND-CUYAHOGA OH 41.41N 81.85W Elev. 791 ft 142 PM EDT Sun May 26 2024 Date 05/26/24 Mon 05/27/24 Tue 05/28/24 Wed EDT 3hrly 17 20 23 02 05 08 11 14 17 20 23 02 05 08 11 14 17 20 23 02 05 08 UTC 3hrly 21 00 03 06 09 12 15 18 21 00 03 06 09 12 15 18 21 00 03 06 09 12 Min/Max 66 76 59 74 56 Temp 83 75 69 68 67 67 73 76 74 68 63 61 59 62 68 72 73 69 63 60 57 58 Dewpt 61 63 64 64 63 64 65 63 60 57 55 55 54 56 57 54 55 54 54 53 52 53 RH 47 66 84 87 87 90 76 64 62 68 75 81 83 81 68 53 53 59 72 78 83 83 Wind dir SE S S S S S SW SW W W W W SW SW W W W W W W NW NW Wind spd 13 14 11 12 13 14 16 16 17 17 14 12 10 11 11 13 12 9 9 9 9 10 Wind gust 26 27 27 26 Clouds OV OV B2 OV OV B2 B2 B1 B1 B1 B1 SC SC SC SC SC SC B1 B1 B1 B1 B1 PoP 12hr 90 60 20 60 70 QPF 12hr 0.21 0.15 0 0.04 0.05 Snow 12hr 00-00 00-00 00-00 Rain shwrs S D C C L L C S S C C L L L L L L C Tstms S D C C L L C S S S C C S C S S Heat index 83 Max heat 84 Date 05/29 Thu 05/30/24 Fri 05/31/24 Sat 06/01/24 Sun 06/02/24 EDT 6hrly 14 20 02 08 14 20 02 08 14 20 02 08 14 20 02 08 14 20 UTC 6hrly 18 00 06 12 18 00 06 12 18 00 06 12 18 00 06 12 18 00 Max/Min 66 50 68 51 73 54 80 61 79 Temp 64 62 53 54 66 65 54 55 71 70 57 59 78 76 65 64 77 75 Dewpt 50 43 41 44 43 42 41 44 45 46 45 48 50 53 52 57 60 60 PWind dir NW N NW N NW SE S S S Wind char GN LT GN LT LT LT LT LT GN Avg clouds B1 SC FW FW CL CL CL FW FW FW FW FW SC SC SC B1 B1 B1 PoP 12hr 50 0 0 0 0 10 20 30 30 Rain shwrs C S S C C C C Tstms S S S S S C $$ OHZ029-270800- MANSFIELD-RICHLAND OH 40.82N 82.52W Elev. 1297 ft 142 PM EDT Sun May 26 2024 Date 05/26/24 Mon 05/27/24 Tue 05/28/24 Wed EDT 3hrly 17 20 23 02 05 08 11 14 17 20 23 02 05 08 11 14 17 20 23 02 05 08 UTC 3hrly 21 00 03 06 09 12 15 18 21 00 03 06 09 12 15 18 21 00 03 06 09 12 Min/Max 65 74 57 72 53 Temp 80 69 67 66 66 67 70 74 73 68 60 58 57 60 66 70 71 68 59 56 54 55 Dewpt 60 63 63 63 62 63 63 61 58 55 53 53 53 54 54 52 52 52 51 50 50 50 RH 51 81 87 90 87 87 78 64 59 63 78 83 86 81 65 53 51 57 75 80 86 83 Wind dir SE S S S S SW SW SW W W W W SW SW W W W W W W W W Wind spd 14 11 13 13 13 14 16 16 18 14 12 9 9 10 12 13 12 8 6 8 9 10 Wind gust 27 29 25 Clouds OV OV B2 OV OV B2 B2 B1 B1 SC SC SC SC SC SC SC SC SC SC SC SC SC PoP 12hr 70 50 10 50 50 QPF 12hr 0.25 0.06 0 0.04 0.02 Snow 12hr 00-00 00-00 00-00 Rain shwrs C L C L L C C S C C C C C C C C C Tstms C L C L L C C S S S C C S C Heat index 81 Max heat 82 Svr Tstorm A Date 05/29 Thu 05/30/24 Fri 05/31/24 Sat 06/01/24 Sun 06/02/24 EDT 6hrly 14 20 02 08 14 20 02 08 14 20 02 08 14 20 02 08 14 20 UTC 6hrly 18 00 06 12 18 00 06 12 18 00 06 12 18 00 06 12 18 00 Max/Min 66 45 68 46 74 51 79 60 79 Temp 63 61 49 50 66 64 49 52 71 69 54 57 76 74 62 63 77 75 Dewpt 48 43 41 41 40 40 39 41 42 46 43 46 48 53 52 55 57 57 PWind dir NW NW NW NE NE SE S S SW Wind char GN LT LT LT LT LT LT LT GN Avg clouds B1 SC FW FW CL CL CL CL CL FW FW FW SC SC B1 B1 B1 SC PoP 12hr 50 0 0 0 0 10 20 30 40 Rain shwrs C C S C C S C Tstms S C C S S C $$ OHZ036-270800- MARION-MARION OH 40.62N 83.06W Elev. 993 ft 142 PM EDT Sun May 26 2024 Date 05/26/24 Mon 05/27/24 Tue 05/28/24 Wed EDT 3hrly 17 20 23 02 05 08 11 14 17 20 23 02 05 08 11 14 17 20 23 02 05 08 UTC 3hrly 21 00 03 06 09 12 15 18 21 00 03 06 09 12 15 18 21 00 03 06 09 12 Min/Max 65 75 57 73 54 Temp 80 70 69 67 66 66 70 74 74 69 61 59 57 60 68 71 72 69 61 57 54 56 Dewpt 62 64 64 64 63 63 63 60 58 55 55 54 54 56 55 52 52 52 52 52 50 51 RH 54 81 84 90 90 90 78 62 57 61 81 83 90 87 63 51 49 55 72 83 86 83 Wind dir S S S S S SW SW SW W W W W SW SW W W W W W W W W Wind spd 14 11 13 13 13 16 16 17 18 14 9 8 8 10 12 13 13 9 9 6 9 10 Wind gust 27 29 Clouds OV OV B2 OV OV B2 B2 B1 B1 SC FW SC FW SC FW SC SC SC SC SC SC SC PoP 12hr 90 50 10 50 40 QPF 12hr 0.25 0.05 0 0.03 0.01 Snow 12hr 00-00 00-00 00-00 Rain shwrs D C L D L C C S S C C C C C C C Tstms D C L D L C C S S C C S S Heat index 81 Max heat 83 Svr Tstorm A Date 05/29 Thu 05/30/24 Fri 05/31/24 Sat 06/01/24 Sun 06/02/24 EDT 6hrly 14 20 02 08 14 20 02 08 14 20 02 08 14 20 02 08 14 20 UTC 6hrly 18 00 06 12 18 00 06 12 18 00 06 12 18 00 06 12 18 00 Max/Min 68 47 70 47 76 53 80 61 80 Temp 65 63 50 51 68 67 51 52 73 71 56 57 77 76 63 63 78 76 Dewpt 48 46 43 43 40 42 41 44 43 47 45 48 49 53 54 57 58 59 PWind dir NW NW N NE NE SE S S SW Wind char GN LT LT LT LT LT GN LT GN Avg clouds SC SC FW FW CL CL CL CL CL FW FW FW SC SC SC B1 B1 SC PoP 12hr 40 0 0 0 0 10 20 30 40 Rain shwrs C C S C C S C Tstms S S C S S C $$ OHZ003-270800- TOLEDO-LUCAS OH 41.59N 83.81W Elev. 684 ft 142 PM EDT Sun May 26 2024 Date 05/26/24 Mon 05/27/24 Tue 05/28/24 Wed EDT 3hrly 17 20 23 02 05 08 11 14 17 20 23 02 05 08 11 14 17 20 23 02 05 08 UTC 3hrly 21 00 03 06 09 12 15 18 21 00 03 06 09 12 15 18 21 00 03 06 09 12 Min/Max 64 73 56 75 53 Temp 80 69 67 68 67 66 69 73 72 68 62 58 56 60 69 74 72 68 61 56 54 55 Dewpt 61 62 63 64 63 62 59 57 55 53 53 53 53 54 52 51 50 49 51 51 50 49 RH 52 78 87 87 87 87 70 57 55 59 72 83 90 81 55 44 46 51 70 83 86 80 Wind dir SE SE S S S SW SW W W W W W SW W W W W W W W W NW Wind spd 12 9 10 11 10 12 16 18 20 16 11 8 8 9 10 13 13 10 9 8 8 9 Wind gust 31 33 27 Clouds OV B2 B2 OV OV B2 B2 B1 B1 SC FW SC SC SC FW FW SC SC SC SC SC SC PoP 12hr 60 20 20 50 40 QPF 12hr 0.25 0.01 0 0.03 0 Snow 12hr 00-00 00-00 00-00 Rain shwrs D L C C C S S S C C C C C C C Tstms D L C C C S S C C S S Heat index 81 Max heat 82 Date 05/29 Thu 05/30/24 Fri 05/31/24 Sat 06/01/24 Sun 06/02/24 EDT 6hrly 14 20 02 08 14 20 02 08 14 20 02 08 14 20 02 08 14 20 UTC 6hrly 18 00 06 12 18 00 06 12 18 00 06 12 18 00 06 12 18 00 Max/Min 70 46 72 48 79 54 82 61 82 Temp 67 65 50 50 69 68 52 53 75 74 57 59 79 77 63 64 79 77 Dewpt 44 41 41 40 37 40 41 44 41 45 46 48 47 51 55 57 55 55 PWind dir NW N N N SW S S S SW Wind char GN LT LT LT LT LT LT LT GN Avg clouds SC FW FW FW CL CL CL CL FW FW FW SC SC SC B1 B1 B1 SC PoP 12hr 30 0 0 0 5 10 20 30 30 Rain shwrs C S S C C S C Tstms S C S S C $$ OHZ009-270800- SANDUSKY-ERIE OH 41.43N 82.65W Elev. 580 ft 142 PM EDT Sun May 26 2024 Date 05/26/24 Mon 05/27/24 Tue 05/28/24 Wed EDT 3hrly 17 20 23 02 05 08 11 14 17 20 23 02 05 08 11 14 17 20 23 02 05 08 UTC 3hrly 21 00 03 06 09 12 15 18 21 00 03 06 09 12 15 18 21 00 03 06 09 12 Min/Max 65 75 58 74 56 Temp 78 71 68 68 66 66 73 75 72 67 62 60 58 62 69 73 73 69 63 59 57 58 Dewpt 63 63 64 64 63 64 64 62 59 56 55 55 55 56 56 55 55 55 54 53 52 52 RH 60 76 87 87 90 93 73 64 64 68 78 84 90 81 63 53 53 61 72 80 83 80 Wind dir E S S S S SW SW SW W W W W SW W W W W W W W NW NW Wind spd 13 13 12 12 12 14 17 18 20 19 16 13 11 12 12 13 11 10 11 10 11 12 Wind gust 28 32 31 Clouds OV OV B2 OV OV B2 B2 B1 B1 B1 SC SC SC SC SC SC SC B1 B1 B1 B1 B1 PoP 12hr 80 40 20 60 50 QPF 12hr 0.25 0.05 0 0.05 0.03 Snow 12hr 00-00 00-00 00-00 Rain shwrs C D C C C C C S C C L L C C C C C Tstms C D C C C C C S S C C S C S S Date 05/29 Thu 05/30/24 Fri 05/31/24 Sat 06/01/24 Sun 06/02/24 EDT 6hrly 14 20 02 08 14 20 02 08 14 20 02 08 14 20 02 08 14 20 UTC 6hrly 18 00 06 12 18 00 06 12 18 00 06 12 18 00 06 12 18 00 Max/Min 67 52 69 53 73 56 78 61 79 Temp 65 63 55 56 66 66 57 57 70 70 59 60 76 74 65 65 77 75 Dewpt 49 45 43 44 43 42 43 46 45 47 47 49 52 56 55 58 61 61 PWind dir NW N N NE NE SE SE S SW Wind char GN GN LT LT LT LT LT GN GN Avg clouds B1 SC FW FW CL CL CL CL FW FW FW SC SC SC B1 B1 B1 SC PoP 12hr 40 0 0 0 0 10 20 30 40 Rain shwrs C S S C C S C Tstms S S S S S C $$ OHZ017-270800- FINDLAY-HANCOCK OH 41.01N 83.67W Elev. 813 ft 142 PM EDT Sun May 26 2024 Date 05/26/24 Mon 05/27/24 Tue 05/28/24 Wed EDT 3hrly 17 20 23 02 05 08 11 14 17 20 23 02 05 08 11 14 17 20 23 02 05 08 UTC 3hrly 21 00 03 06 09 12 15 18 21 00 03 06 09 12 15 18 21 00 03 06 09 12 Min/Max 65 75 58 75 54 Temp 82 70 69 68 66 67 72 75 74 70 62 60 58 61 69 73 75 70 62 58 54 57 Dewpt 61 62 63 63 62 62 60 58 56 54 53 53 53 53 52 51 50 49 50 49 49 49 RH 49 76 81 84 87 84 66 55 53 57 72 78 83 75 55 46 41 47 65 72 83 75 Wind dir S S S S S SW SW W W W W W SW W W W W NW W W W NW Wind spd 14 11 12 14 12 14 17 19 19 14 10 9 8 11 12 13 14 10 9 8 9 10 Wind gust 31 32 25 Clouds OV B2 B2 OV B2 B2 B2 B1 B1 SC FW SC SC SC FW SC SC SC SC SC SC SC PoP 12hr 70 30 10 50 30 QPF 12hr 0.30 0.05 0 0.02 0 Snow 12hr 00-00 00-00 00-00 Rain shwrs D C L L C C S S C C C C C C C Tstms D C L L C C S C C S Heat index 82 Max heat 84 Svr Tstorm A Date 05/29 Thu 05/30/24 Fri 05/31/24 Sat 06/01/24 Sun 06/02/24 EDT 6hrly 14 20 02 08 14 20 02 08 14 20 02 08 14 20 02 08 14 20 UTC 6hrly 18 00 06 12 18 00 06 12 18 00 06 12 18 00 06 12 18 00 Max/Min 70 47 72 49 79 55 82 62 82 Temp 67 65 52 52 69 69 53 54 75 74 58 59 79 77 65 65 80 78 Dewpt 46 43 42 41 39 41 40 43 42 44 44 47 47 52 54 56 56 56 PWind dir NW NW N NE E SE S S SW Wind char GN LT LT LT LT LT GN GN GN Avg clouds SC SC FW FW CL CL CL CL FW FW FW FW SC SC B1 B1 B1 SC PoP 12hr 30 0 0 0 5 10 20 30 30 Rain shwrs C C S C C S C Tstms S C S S C $$