FOUS51 KCLE 150747 PFMCLE Point Forecast Matrices National Weather Service CLEVELAND, OHIO 247 AM EST Mon Dec 15 2025 PAZ001-152100- ERIE-ERIE PA 42.08N 80.18W Elev. 733 ft 247 AM EST Mon Dec 15 2025 Date Mon 12/15/25 Tue 12/16/25 Wed 12/17/25 EST 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 26 16 34 29 40 Temp 24 25 23 22 23 20 20 18 17 18 22 29 33 30 31 33 34 36 38 39 38 35 Dewpt 16 16 16 13 12 11 12 14 14 13 13 15 17 18 20 22 25 27 29 31 30 29 RH 71 68 74 68 62 67 71 84 88 80 68 55 51 60 63 63 69 69 70 73 73 78 Wind dir W W SW SW SW SW SW SW S S S S S S S S SW SW SW W W SW Wind spd 10 10 14 16 14 14 12 10 10 10 12 14 14 14 17 18 18 17 16 14 11 8 Wind gust 26 28 29 28 27 Clouds OV OV OV OV OV B1 B2 B2 OV B2 SC B1 B1 B1 SC SC B2 B2 OV B2 B2 B2 PoP 12hr 70 40 0 5 10 QPF 12hr 0.06 0.04 0 0 0 Snow 12hr 1 T 00-00 Snowshwrs C C L L C C C Wind chill 13 14 10 9 9 7 7 6 5 6 10 18 22 19 19 22 23 26 29 30 30 28 Min chill 13 9 7 6 5 6 19 19 22 27 28 Lk Eff Snow W Date Thu 12/18/25 Fri 12/19/25 Sat 12/20/25 Sun 12/21/25 EST 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 30 47 22 28 21 41 30 37 Temp 32 37 45 43 35 24 27 24 23 26 38 39 37 34 35 31 Dewpt 26 29 35 36 30 21 16 14 14 16 21 26 27 28 27 24 PWind dir S S SW W SW S SW W Wind char GN BZ BZ BZ GN BZ GN GN Avg clouds B1 B2 B2 OV OV B2 B2 B2 B2 B2 B2 OV B2 B2 B2 B2 PoP 12hr 5 90 90 50 10 30 50 30 Rain C D D C S C C C C S Snow D C Snowshwrs C C $$ OHZ033-152100- YOUNGSTOWN/WARREN-TRUMBULL OH 41.25N 80.67W Elev. 1196 ft 247 AM EST Mon Dec 15 2025 Date Mon 12/15/25 Tue 12/16/25 Wed 12/17/25 EST 3hrly 04 07 10 13 16 19 22 01 04 07 10 13 16 19 22 01 04 07 10 13 16 19 UTC 3hrly 09 12 15 18 21 00 03 06 09 12 15 18 21 00 03 06 09 12 15 18 21 00 Max/Min 20 11 31 26 39 Temp 14 13 15 17 19 17 15 14 12 13 20 28 31 27 28 31 32 33 36 37 38 32 Dewpt 12 11 10 10 9 8 9 9 9 8 12 15 17 17 20 21 25 27 29 30 30 28 RH 92 91 80 73 64 67 77 80 87 80 71 58 56 65 71 66 75 78 75 75 73 85 Wind dir W SW SW SW SW SW SW SW SW S S S S S S S SW SW SW SW W SW Wind spd 8 10 10 12 11 10 9 6 6 6 9 11 10 11 12 12 12 12 11 11 8 5 Wind gust 23 Clouds OV OV OV OV B2 SC SC FW SC FW SC SC SC SC SC SC B2 B2 OV OV B2 B1 PoP 12hr 10 0 0 0 5 QPF 12hr 0 0 0 0 0 Snow 12hr 00-00 00-00 00-00 Wind chill 3 1 2 4 7 5 3 3 1 2 9 18 22 17 17 21 23 24 28 30 32 26 Min chill 1 2 5 3 1 3 17 16 22 26 26 Date Thu 12/18/25 Fri 12/19/25 Sat 12/20/25 Sun 12/21/25 EST 6hrly 01 07 13 19 01 07 13 19 01 07 13 19 01 07 13 19 UTC 6hrly 06 12 18 00 06 12 18 00 06 12 18 00 06 12 18 00 Min/Max 27 47 19 27 18 41 29 38 Temp 30 34 45 43 35 21 25 22 21 24 38 38 36 33 36 30 Dewpt 27 30 37 39 29 17 13 12 12 14 20 24 29 29 27 25 PWind dir S S SW W SW S SW W Wind char GN BZ GN GN GN GN GN GN Avg clouds B1 B2 OV OV OV B2 B2 B2 B2 B2 B2 B2 B2 B2 B2 B2 PoP 12hr 5 90 80 30 10 30 50 30 Rain C D D S C C C C S Snow D C Snowshwrs C S $$ OHZ032-152100- AKRON/CANTON-SUMMIT OH 40.92N 81.44W Elev. 1228 ft 247 AM EST Mon Dec 15 2025 Date Mon 12/15/25 Tue 12/16/25 Wed 12/17/25 EST 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 20 13 32 27 40 Temp 10 10 13 18 20 18 16 15 13 14 21 29 32 28 28 31 32 33 36 38 38 32 Dewpt 10 9 9 10 9 9 10 9 9 10 13 17 19 19 21 24 26 28 31 33 32 29 RH 100 96 84 70 62 67 77 77 84 84 71 60 58 68 75 75 78 82 82 82 79 88 Wind dir W SW SW SW SW SW SW SW SW S S S S S SW SW SW SW SW SW W SW Wind spd 8 8 10 12 11 10 8 5 5 6 9 11 11 12 13 13 13 13 11 10 8 6 Wind gust 21 23 25 26 26 25 21 Clouds B2 OV OV OV B1 SC SC SC FW FW SC SC SC SC SC SC B1 B2 B2 B2 B1 B1 PoP 12hr 10 0 0 0 5 QPF 12hr 0 0 0 0 0 Snow 12hr 00-00 00-00 00-00 Wind chill -2 -2 0 4 7 6 6 6 4 4 10 19 22 17 18 21 22 23 28 31 31 26 Min chill -3 -2 5 5 2 3 17 17 21 24 26 Date Thu 12/18/25 Fri 12/19/25 Sat 12/20/25 Sun 12/21/25 EST 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 28 48 19 27 20 43 32 39 Temp 31 36 46 44 34 21 26 23 22 26 39 40 37 34 38 32 Dewpt 29 33 40 40 30 16 13 12 12 16 23 27 31 31 30 27 PWind dir S S SW W SW S SW W Wind char GN BZ BZ GN GN GN GN GN Avg clouds B1 B2 B2 OV B2 B2 B2 B1 B1 B2 B2 B2 B2 B2 B2 B1 PoP 12hr 10 90 70 10 10 30 50 30 Rain C D L S C C C C S Snow L S $$ OHZ031-152100- WOOSTER-WAYNE OH 40.87N 81.89W Elev. 1136 ft 247 AM EST Mon Dec 15 2025 Date Mon 12/15/25 Tue 12/16/25 Wed 12/17/25 EST 3hrly 04 07 10 13 16 19 22 01 04 07 10 13 16 19 22 01 04 07 10 13 16 19 UTC 3hrly 09 12 15 18 21 00 03 06 09 12 15 18 21 00 03 06 09 12 15 18 21 00 Max/Min 20 12 32 26 40 Temp 8 9 13 18 19 17 17 15 12 14 21 29 32 28 29 31 32 33 36 38 38 32 Dewpt 8 8 9 9 9 9 10 10 10 10 14 17 20 20 22 25 27 29 32 33 32 30 RH 100 96 84 67 64 70 73 80 91 84 74 60 61 71 75 78 81 85 85 82 79 92 Wind dir W SW SW SW SW SW SW SW SW S S S S S S SW SW SW SW W W S Wind spd 6 8 11 13 12 10 6 5 5 5 10 12 12 13 13 14 14 13 12 10 8 5 Wind gust 24 25 25 25 24 Clouds B2 OV OV OV B1 SC SC FW FW FW FW SC SC SC SC SC B1 OV B2 B2 B1 B1 PoP 12hr 10 0 0 0 5 QPF 12hr 0 0 0 0 0 Snow 12hr 00-00 00-00 00-00 Wind chill -4 -3 -1 4 7 5 7 6 4 4 10 19 22 17 17 21 22 24 28 31 32 26 Min chill -4 -2 5 4 3 3 16 16 21 24 25 Date Thu 12/18/25 Fri 12/19/25 Sat 12/20/25 Sun 12/21/25 EST 6hrly 01 07 13 19 01 07 13 19 01 07 13 19 01 07 13 19 UTC 6hrly 06 12 18 00 06 12 18 00 06 12 18 00 06 12 18 00 Min/Max 27 48 18 27 18 43 30 39 Temp 30 36 45 43 32 20 26 22 21 26 40 40 36 33 38 31 Dewpt 29 33 40 40 29 16 12 13 12 16 23 28 31 32 30 27 PWind dir S S W W S S SW NW Wind char GN BZ BZ GN GN GN GN GN Avg clouds B1 B2 B2 OV B2 B2 B2 B1 B1 B1 B2 B2 B2 B2 B2 B1 PoP 12hr 10 90 60 10 10 30 40 30 Rain C D L C C C C S Snow L $$ OHZ011-152100- CLEVELAND-CUYAHOGA OH 41.41N 81.85W Elev. 791 ft 247 AM EST Mon Dec 15 2025 Date Mon 12/15/25 Tue 12/16/25 Wed 12/17/25 EST 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 22 15 34 29 40 Temp 14 13 16 20 22 19 18 16 15 16 23 31 33 29 30 32 33 35 38 40 38 34 Dewpt 13 11 11 11 11 10 12 12 11 11 14 19 22 21 24 26 28 29 32 33 32 30 RH 96 91 80 67 62 67 77 84 84 80 68 61 63 72 78 78 82 78 79 76 79 85 Wind dir SW SW SW SW SW SW SW SW SW S S S S S S SW SW SW SW W SW S Wind spd 9 10 12 14 14 11 9 6 5 6 10 13 13 12 13 13 13 12 12 11 10 5 Wind gust 25 23 24 26 27 28 27 25 Clouds OV OV OV OV B1 B1 B1 SC SC SC SC SC SC SC SC SC B2 OV B2 B2 B2 B1 PoP 12hr 10 0 0 5 5 QPF 12hr 0 0 0 0 0 Snow 12hr 00-00 00-00 00-00 Wind chill 2 0 3 7 9 8 8 7 7 6 13 21 24 19 20 22 23 26 30 32 31 28 Min chill -1 0 6 6 6 7 19 19 22 27 28 Date Thu 12/18/25 Fri 12/19/25 Sat 12/20/25 Sun 12/21/25 EST 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 30 49 21 29 21 43 31 39 Temp 32 37 47 43 32 22 27 24 22 27 40 40 37 34 37 32 Dewpt 30 34 40 40 28 18 15 14 13 17 24 28 31 31 29 27 PWind dir S S W W SW S SW NW Wind char GN BZ BZ GN GN GN GN GN Avg clouds B1 B2 OV OV B2 B2 B2 B2 B1 B2 B2 B2 B2 B2 B2 B1 PoP 12hr 10 90 60 40 10 30 40 30 Rain L D L S C C C C S Snow L S Snowshwrs C S $$ OHZ029-152100- MANSFIELD-RICHLAND OH 40.82N 82.52W Elev. 1297 ft 247 AM EST Mon Dec 15 2025 Date Mon 12/15/25 Tue 12/16/25 Wed 12/17/25 EST 3hrly 04 07 10 13 16 19 22 01 04 07 10 13 16 19 22 01 04 07 10 13 16 19 UTC 3hrly 09 12 15 18 21 00 03 06 09 12 15 18 21 00 03 06 09 12 15 18 21 00 Max/Min 19 14 33 29 38 Temp 8 9 13 17 19 17 18 17 15 16 22 29 32 29 31 33 34 34 35 37 37 32 Dewpt 7 6 7 6 7 8 10 9 9 10 13 17 18 21 23 25 27 29 30 31 30 29 RH 96 87 76 61 59 67 70 70 77 77 68 60 56 72 72 72 75 82 82 79 75 88 Wind dir W SW SW SW SW SW SW SW SW S S S S S SW SW SW SW SW W SW S Wind spd 8 9 11 13 12 10 8 6 6 8 10 12 13 13 14 14 14 14 11 10 8 6 Wind gust 24 20 26 26 27 27 25 21 Clouds B2 OV OV OV B2 B1 FW FW FW FW FW SC SC SC SC SC B1 B2 B2 B2 B1 B1 PoP 12hr 10 0 0 0 5 QPF 12hr 0 0 0 0 0 Snow 12hr 00-00 00-00 00-00 Wind chill -5 -4 -1 4 6 5 8 7 5 5 11 19 22 18 20 23 24 25 27 30 31 26 Min chill -5 -3 4 6 5 6 18 18 23 25 26 Date Thu 12/18/25 Fri 12/19/25 Sat 12/20/25 Sun 12/21/25 EST 6hrly 01 07 13 19 01 07 13 19 01 07 13 19 01 07 13 19 UTC 6hrly 06 12 18 00 06 12 18 00 06 12 18 00 06 12 18 00 Min/Max 29 47 18 27 20 42 30 38 Temp 32 37 45 42 31 19 25 22 23 27 39 39 37 33 36 30 Dewpt 29 34 39 38 25 14 10 11 12 17 21 27 30 30 28 27 PWind dir S S W W S S SW NW Wind char GN BZ BZ GN GN GN GN GN Avg clouds B1 B2 B2 OV B2 B2 B1 B1 B1 B1 B2 B2 B2 B2 B2 B1 PoP 12hr 10 90 50 10 10 30 40 30 Rain L D C C C C C S Snow C $$ OHZ036-152100- MARION-MARION OH 40.62N 83.06W Elev. 993 ft 247 AM EST Mon Dec 15 2025 Date Mon 12/15/25 Tue 12/16/25 Wed 12/17/25 EST 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 20 13 34 28 40 Temp 6 8 12 18 20 18 17 15 13 15 22 30 32 29 30 31 33 33 37 38 38 31 Dewpt 5 4 4 5 8 9 10 9 9 10 13 18 21 22 23 25 27 29 31 32 31 29 RH 96 83 70 56 59 67 73 77 84 80 68 60 63 75 75 78 78 85 79 79 76 92 Wind dir SW S SW SW SW SW SW SW S S S S S S S SW SW SW SW SW SW S Wind spd 5 8 11 14 13 10 6 4 5 8 10 12 13 13 13 13 13 12 10 9 8 8 Wind gust 25 25 25 24 Clouds B1 OV B2 B2 B2 B1 FW FW CL FW SC SC SC SC SC SC B1 B2 B2 B2 B1 B1 PoP 12hr 5 0 0 0 0 QPF 12hr 0 0 0 0 0 Snow 12hr 00-00 00-00 00-00 Wind chill -5 -4 -2 4 6 6 7 8 4 4 11 20 22 18 19 21 23 24 29 32 32 24 Min chill -5 -4 5 5 3 4 18 18 22 26 24 Date Thu 12/18/25 Fri 12/19/25 Sat 12/20/25 Sun 12/21/25 EST 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 29 47 17 28 19 44 30 40 Temp 31 37 45 41 30 19 27 23 22 26 41 39 36 33 38 31 Dewpt 29 34 39 37 24 13 11 11 12 17 22 29 31 31 29 27 PWind dir S S W W S S SW NW Wind char GN BZ GN GN GN GN GN GN Avg clouds B1 B2 OV OV B2 B2 B1 B1 B1 B1 B2 B2 B2 B2 B2 B1 PoP 12hr 10 90 40 10 10 20 40 20 Rain L D C S C C S S Snow C $$ OHZ003-152100- TOLEDO-LUCAS OH 41.59N 83.81W Elev. 684 ft 247 AM EST Mon Dec 15 2025 Date Mon 12/15/25 Tue 12/16/25 Wed 12/17/25 EST 3hrly 04 07 10 13 16 19 22 01 04 07 10 13 16 19 22 01 04 07 10 13 16 19 UTC 3hrly 09 12 15 18 21 00 03 06 09 12 15 18 21 00 03 06 09 12 15 18 21 00 Max/Min 21 13 34 29 40 Temp 12 11 13 19 21 20 18 16 14 15 22 31 33 31 30 33 34 34 36 39 37 33 Dewpt 8 4 2 3 6 8 10 11 10 10 13 17 20 22 25 27 29 30 31 31 30 29 RH 84 73 61 49 52 59 70 80 84 80 68 56 58 69 81 78 82 85 82 73 75 85 Wind dir SW SW SW SW SW SW SW SW SW S S SW S SW SW SW SW SW W W SW S Wind spd 9 10 13 16 13 10 6 4 4 5 10 13 13 13 14 14 14 12 10 10 8 5 Wind gust 26 24 25 27 27 25 Clouds B2 OV OV B2 B1 SC SC SC SC SC SC SC SC SC SC B2 B2 B2 B1 B1 SC B1 PoP 12hr 10 0 0 0 0 QPF 12hr 0 0 0 0 0 Snow 12hr 00-00 00-00 00-00 Wind chill -1 -3 -2 4 7 9 9 9 7 6 12 21 24 21 19 23 25 25 29 32 31 Min chill -3 -5 6 8 6 4 21 19 24 26 28 Date Thu 12/18/25 Fri 12/19/25 Sat 12/20/25 Sun 12/21/25 EST 6hrly 01 07 13 19 01 07 13 19 01 07 13 19 01 07 13 19 UTC 6hrly 06 12 18 00 06 12 18 00 06 12 18 00 06 12 18 00 Min/Max 30 47 19 27 21 41 27 36 Temp 32 37 45 39 27 20 26 24 24 27 40 38 34 31 35 30 Dewpt 30 35 41 34 20 12 12 13 13 17 22 27 29 26 26 24 PWind dir S S W W S SW W NW Wind char GN BZ BZ GN GN GN GN LT Avg clouds B2 B2 OV OV B2 B2 B1 B1 B1 B2 B2 B2 B2 B2 B1 B1 PoP 12hr 10 90 30 10 10 20 30 20 Rain D D C S C S S Snow C $$ OHZ009-152100- SANDUSKY-ERIE OH 41.43N 82.65W Elev. 580 ft 247 AM EST Mon Dec 15 2025 Date Mon 12/15/25 Tue 12/16/25 Wed 12/17/25 EST 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 23 16 35 29 40 Temp 14 13 16 22 23 20 19 17 17 17 24 32 34 29 30 32 33 33 37 39 38 33 Dewpt 12 9 9 10 11 11 12 12 12 12 16 20 23 23 25 26 28 29 33 34 33 31 RH 92 84 73 59 59 67 74 80 80 80 71 61 64 78 81 78 82 85 85 82 82 92 Wind dir SW SW SW SW SW SW SW SW SW S S S S S SW SW SW SW SW W SW S Wind spd 6 9 12 14 13 10 6 5 5 6 9 12 13 12 13 13 12 11 10 10 6 5 Wind gust 17 23 25 24 20 17 24 25 27 28 26 24 20 Clouds B2 OV OV OV B1 SC SC SC FW SC SC SC SC SC SC B1 B2 B2 B2 B1 B1 B1 PoP 12hr 10 0 0 0 5 QPF 12hr 0 0 0 0 0 Snow 12hr 00-00 00-00 00-00 Wind chill 3 1 2 8 10 9 10 9 9 8 14 22 25 19 20 22 24 25 30 33 32 Min chill 1 0 9 9 8 8 19 19 23 26 28 Date Thu 12/18/25 Fri 12/19/25 Sat 12/20/25 Sun 12/21/25 EST 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 30 48 19 29 21 43 30 38 Temp 32 37 46 42 30 20 28 25 24 28 40 39 36 32 37 31 Dewpt 30 34 42 39 24 15 16 15 14 17 25 29 30 30 30 27 PWind dir S S W W SW S SW NW Wind char GN BZ GN GN LT GN LT GN Avg clouds B1 B2 OV OV B2 B2 B2 B1 B2 B2 B2 B2 B2 B2 B2 B1 PoP 12hr 10 90 50 10 10 30 40 20 Rain L D C C C C S S Snow C $$ OHZ017-152100- FINDLAY-HANCOCK OH 41.01N 83.67W Elev. 813 ft 247 AM EST Mon Dec 15 2025 Date Mon 12/15/25 Tue 12/16/25 Wed 12/17/25 EST 3hrly 04 07 10 13 16 19 22 01 04 07 10 13 16 19 22 01 04 07 10 13 16 19 UTC 3hrly 09 12 15 18 21 00 03 06 09 12 15 18 21 00 03 06 09 12 15 18 21 00 Max/Min 21 13 34 29 40 Temp 7 8 12 19 21 19 17 16 14 16 23 32 34 30 31 33 34 34 36 38 38 34 Dewpt 5 3 4 5 8 9 11 11 11 11 15 19 22 23 25 27 29 30 32 32 31 29 RH 91 79 70 54 56 64 77 80 88 80 71 58 61 75 78 78 82 85 85 79 76 82 Wind dir SW SW SW SW SW SW SW SW S S S S S S SW SW SW SW SW W SW S Wind spd 9 10 13 16 13 10 8 5 6 8 11 13 14 13 14 16 16 14 12 10 9 8 Wind gust 26 24 25 27 28 27 Clouds B1 OV OV B2 B1 B1 FW FW FW FW FW FW SC SC SC B1 B2 B2 B2 B1 SC B1 PoP 12hr 10 0 0 0 0 QPF 12hr 0 0 0 0 0 Snow 12hr 00-00 00-00 00-00 Wind chill -6 -6 -3 4 7 7 7 6 4 5 12 22 23 19 20 22 24 25 28 31 31 27 Min chill -7 -6 6 6 4 5 19 19 23 25 27 Date Thu 12/18/25 Fri 12/19/25 Sat 12/20/25 Sun 12/21/25 EST 6hrly 01 07 13 19 01 07 13 19 01 07 13 19 01 07 13 19 UTC 6hrly 06 12 18 00 06 12 18 00 06 12 18 00 06 12 18 00 Min/Max 30 48 18 28 21 44 29 38 Temp 33 38 47 40 28 19 27 24 24 27 41 40 36 32 37 31 Dewpt 30 35 41 36 22 13 12 12 12 17 23 29 31 29 27 26 PWind dir S S W W S S SW NW Wind char GN BZ BZ GN GN BZ GN GN Avg clouds B1 B2 OV OV B2 B2 B2 B1 B1 B1 B2 B2 B2 B2 B2 B1 PoP 12hr 10 90 30 10 5 20 30 20 Rain D D C S C C S S Snow C $$