fzus63 kdtx 311945
glflh 
expires:202108010800;;764862

open lake forecast for lake huron
national weather service detroit/pontiac mi
345 pm edt sat jul 31 2021

for waters beyond five nautical miles off shore on lake huron

waves are the significant wave height - the average of the highest
1/3 of the wave spectrum. occasional wave height is the average of
the highest 1/10 of the wave spectrum.

.synopsis...a cold front associated with low pressure, 29.80
inches, will continue dropping southeast across the local waters
through sunday morning. expansive high pressure will then build
to around 30.10 inches across the upper midwest and great lakes
for early to the middle of next week.


lhz362-363-010800-
lake huron from presque isle light to sturgeon point mi beyond
5nm off shore-
lake huron from sturgeon point to alabaster mi beyond 5nm off
shore-
345 pm edt sat jul 31 2021

.tonight...south winds 5 to 10 knots veering to the southwest in
the late evening and early morning...then veering to the
southwest 5 to 10 knots early in the morning. showers likely and
a chance of thunderstorms. waves 1 to 3 feet. 
.sunday...north winds 10 to 15 knots increasing to 15 to 20 knots
early in the afternoon...then decreasing to 10 to 15 knots late
in the afternoon. a chance of waterspouts in the morning. a
chance of showers and thunderstorms. waves 1 to 3 feet building
to 3 to 5 feet in the late morning and afternoon. 
.sunday night...north winds 10 to 15 knots. waves 3 to 5 feet. 
.monday...north winds 5 to 10 knots backing to the northwest in
the late morning and early afternoon...then becoming light and
variable early in the afternoon. waves 2 to 4 feet subsiding to
1 to 3 feet in the late morning and afternoon. 
.monday night...light and variable winds becoming southwest 5 to
10 knots in the late evening and overnight. waves 2 feet or less.
.tuesday...southwest winds 5 to 10 knots backing to the south
late in the afternoon. waves 2 feet or less. 
.wednesday...light and variable winds becoming southeast 5 to
10 knots until early morning. waves 2 feet or less. 
.thursday...south winds 5 to 10 knots. waves 2 feet or less. 


$$

fzus63 kdtx 311945
glflh 
expires:202108010800;;764861

open lake forecast for lake huron
national weather service detroit/pontiac mi
345 pm edt sat jul 31 2021

for waters beyond five nautical miles off shore on lake huron

waves are the significant wave height - the average of the highest
1/3 of the wave spectrum. occasional wave height is the average of
the highest 1/10 of the wave spectrum.

.synopsis...a cold front associated with low pressure, 29.80
inches, will continue dropping southeast across the local waters
through sunday morning. expansive high pressure will then build
to around 30.10 inches across the upper midwest and great lakes
for early to the middle of next week.


lhz361-010800-
lake huron from 5nm east of mackinac bridge to presque isle lt
beyond 5 nm off shore-
345 pm edt sat jul 31 2021

.tonight...west winds 10 to 15 knots veering to the north early
in the morning. a chance of thunderstorms in the evening. a
chance of showers. a chance of waterspouts after midnight. waves
1 to 3 feet. 
.sunday...north winds 10 to 15 knots decreasing to 5 to 10 knots
late in the afternoon. a chance of waterspouts. a chance of
showers. waves 1 to 3 feet. 
.sunday night...northwest winds 10 to 15 knots decreasing to 5 to
10 knots after midnight. waves 1 to 3 feet building to 2 to
4 feet in the late evening and overnight. 
.monday...northwest winds 5 to 10 knots backing to the west early
in the afternoon. waves 2 feet or less. 
.monday night...west winds 5 to 10 knots. waves 2 feet or less. 
.tuesday...southwest winds 5 to 10 knots becoming light and
variable. waves 2 feet or less. 
.wednesday...light and variable winds becoming southeast 5 to
10 knots early in the evening...then veering to the south in the
late evening and early morning. waves 2 feet or less. 
.thursday...southwest winds 5 to 10 knots backing to the south
until early morning. waves 2 feet or less. 


$$

fzus63 kdtx 311945
glflh 
expires:202108010800;;764863

open lake forecast for lake huron
national weather service detroit/pontiac mi
345 pm edt sat jul 31 2021

for waters beyond five nautical miles off shore on lake huron

waves are the significant wave height - the average of the highest
1/3 of the wave spectrum. occasional wave height is the average of
the highest 1/10 of the wave spectrum.

.synopsis...a cold front associated with low pressure, 29.80
inches, will continue dropping southeast across the local waters
through sunday morning. expansive high pressure will then build
to around 30.10 inches across the upper midwest and great lakes
for early to the middle of next week.


lhz462>464-010800-
lake huron from port austin to harbor beach beyond 5nm off shore-
lake huron from harbor beach to port sanilac beyond 5nm off shore-
lake huron from port sanilac to port huron beyond 5nm off shore-
345 pm edt sat jul 31 2021

.tonight...south winds 5 to 10 knots veering to the west after
midnight. a chance of showers in the evening. a chance of
thunderstorms. rain showers likely after midnight. waves 1 to
3 feet. 
.sunday...northwest winds 5 to 10 knots increasing to 10 to
15 knots in the late morning and early afternoon...then becoming
north 15 to 20 knots late in the afternoon. a chance of
waterspouts. showers likely and a chance of thunderstorms. waves
1 to 3 feet building to 3 to 5 feet in the afternoon. 
.sunday night...north winds 15 to 20 knots decreasing to 10 to
15 knots after midnight. a chance of waterspouts in the evening.
waves 4 to 6 feet. waves occasionally around 8 feet. 
.monday...north winds 5 to 10 knots. waves 2 to 4 feet subsiding
to 1 to 3 feet in the late morning and afternoon. 
.monday night...light and variable winds becoming south 5 to
10 knots in the late evening and early morning...then veering to
the southwest after midnight. waves 2 feet or less. 
.tuesday...southwest winds 5 to 10 knots in the morning becoming
light and variable. waves 2 feet or less. 
.wednesday...light and variable winds becoming southeast 5 to
10 knots in the late evening and early morning. waves 2 feet or
less. 
.thursday...south winds 5 to 10 knots. waves 2 feet or less. 


$$

fzus63 kmkx 311930
glflm 
expires:202108010315;;764178

open lake forecast for lake michigan
national weather service milwaukee/sullivan wi
230 pm cdt sat jul 31 2021

for waters beyond five nautical miles of shore on lake michigan.

waves are provided as a range of significant wave heights, which
is the average of the highest 1/3 of the wave, along with the
average height of the highest 10% of the waves which will
occasionally be encountered.

.synopsis... 
low pressure of 29.8 inches will track from northern lower michigan
into lake huron by sunday morning. this will bring a cold front 
through the region through tonight. along the front thunderstorms
will be possible. south to southwest winds will shift to the 
north-northwest behind the front and build into sunday with gusts 
around 25 knots. high pressure of 30.2 inches will then build in 
from the northwest sunday evening into monday resulting in light 
and variable winds for the beginning of next week.

&&


lmz261-362-364-366-563-565-567-868-010315-
lake michigan from seul choix point to rock island passage 5 nm
offshore to mid lake-
lake michigan south of a line from seul choix point to the
mackinac bridge and north of a line from charlevoix mi to south
fox island 5 nm offshore-
lake michigan from charlevoix to point betsie mi 5 nm offshore to
mid lake-
lake michigan from point betsie to manistee mi 5 nm offshore to
mid lake-
lake michigan from rock island passage to sturgeon bay wi-
lake michigan from sturgeon bay to two rivers wi 5 nm offshore to
mid lake-
lake michigan from two rivers to sheboygan wi 5 nm offshore to
mid lake-
lake michigan from pentwater to manistee mi 5 nm offshore to mid
lake-
230 pm cdt sat jul 31 2021

sheboygan wi to pentwater mi north...

.tonight...west winds 10 to 20 kt veering to north 15 to 25 kt.
chance of showers and thunderstorms this evening. haze. waves
2 to 4 ft. 
.sunday...north winds 15 to 25 kt. waves 4 to 6 ft occasionally
to 8 ft. 
.sunday night...north winds 15 to 25 kt diminishing to 5 to
10 kt. waves 3 to 5 ft subsiding to 1 to 3 ft. 
.monday...northwest winds 5 to 10 kt becoming southwest 10 to
15 kt. waves 1 to 2 ft. 
.monday night...southwest winds 10 to 15 kt. waves 1 to 3 ft. 
.tuesday...west winds 10 to 15 kt becoming southwest. waves 1 to
3 ft. 
.tuesday night...southwest winds 5 to 10 kt. waves 1 to 2 ft. 
.wednesday...south winds 5 to 10 kt. waves 1 ft or less. 
.thursday...southwest winds 10 to 20 kt becoming south. waves
2 to 4 ft.  

$$

fzus63 kmkx 311930
glflm 
expires:202108010315;;764179

open lake forecast for lake michigan
national weather service milwaukee/sullivan wi
230 pm cdt sat jul 31 2021

for waters beyond five nautical miles of shore on lake michigan.

waves are provided as a range of significant wave heights, which
is the average of the highest 1/3 of the wave, along with the
average height of the highest 10% of the waves which will
occasionally be encountered.

.synopsis... 
low pressure of 29.8 inches will track from northern lower michigan
into lake huron by sunday morning. this will bring a cold front 
through the region through tonight. along the front thunderstorms
will be possible. south to southwest winds will shift to the 
north-northwest behind the front and build into sunday with gusts 
around 25 knots. high pressure of 30.2 inches will then build in 
from the northwest sunday evening into monday resulting in light 
and variable winds for the beginning of next week.

&&


lmz080-669-671-673-675-777-779-870-872-874-876-878-010315-
lake michigan from michigan city in to st. joseph mi 5 nm
offshore to mid lake-
lake michigan from sheboygan to port washington wi 5 nm offshore
to mid lake-
lake michigan from port washington to north point light wi 5 nm
offshore to mid lake-
lake michigan from north point light to wind point wi 5 nm
offshore to mid lake-
lake michigan from wind point wi to winthrop harbor il 5 nm
offshore to mid lake-
lake michigan from winthrop harbor to wilmette harbor il 5 nm
offshore to mid lake-
lake michigan from wilmette harbor il to michigan city in 5 nm
offshore to mid lake-
lake michigan from whitehall to pentwater mi 5 nm offshore to mid
lake-
lake michigan from grand haven to whitehall mi 5 nm offshore to
mid lake-
lake michigan from holland to grand haven mi 5 nm offshore to mid
lake-
lake michigan from south haven to holland mi 5 nm offshore to mid
lake-
lake michigan from st. joseph to south haven mi 5 nm offshore to
mid lake-
230 pm cdt sat jul 31 2021

sheboygan wi to pentwater mi south...

.tonight...southwest winds 10 to 20 kt veering to north 15 to
25 kt. haze. chance of showers and thunderstorms this evening,
then slight chance of showers and thunderstorms overnight. waves
2 to 4 ft building to 3 to 5 ft. 
.sunday...north winds to 30 kt. waves 4 to 7 ft occasionally to
9 ft. 
.sunday night...north winds to 30 kt becoming northeast 10 to
15 kt. chance of showers overnight. waves 4 to 7 ft occasionally
to 9 ft subsiding to 2 to 4 ft. 
.monday...north winds 5 to 10 kt. waves 2 to 4 ft subsiding to
1 to 2 ft. 
.monday night...southwest winds 5 to 10 kt. waves 1 to 2 ft.
.tuesday...west winds 5 to 10 kt becoming southwest. waves 1 to
2 ft. 
.tuesday night...south winds 5 to 10 kt becoming southwest. waves
1 ft or less. 
.wednesday...southwest winds 5 to 10 kt becoming south. waves
1 ft or less. 
.thursday...southwest winds 10 to 15 kt becoming south. waves
1 to 3 ft.  

$$

fzus63 kmqt 311945
glfls 
expires:202108010345;;764781

open lake forecast for lake superior
national weather service marquette mi
345 pm edt sat jul 31 2021

for waters beyond 5 nautical miles of shore on lake superior.

waves are the significant wave height - the average of the
highest 1/3 of the wave spectrum. occasional wave height is the
average of the highest 1/10 of the wave spectrum.

.synopsis...a 29.9 inch trough will push south out of the upper 
great lakes tonight. this trough will be followed by 30.1 inch 
ridging over lake superior sunday. this ridge will weaken slightly
to 30.0 inches monday night as a weak 29.9 inch trough clips the 
northern shore of the lake. the 30.0 inch ridging will persist 
through the remainder of the week while 29.8 inch troughing 
develops over northern minnesota. 


lsz265-010345-
lake superior west of line from manitou island to marquette mi
beyond 5nm from shore-
345 pm edt sat jul 31 2021

.late this afternoon...north winds 10 to 20 knots. patchy smoke.
isolated showers and thunderstorms. waves calm to 2 feet. 
.tonight...north winds 10 to 20 knots increasing to 15 to
25 knots after midnight. patchy smoke through midnight. isolated
thunderstorms through midnight. isolated showers. waves building
to 3 to 5 feet occasionally to 7 feet. 
.sunday...north winds 15 to 25 knots diminishing to 10 to
20 knots in the afternoon. waves subsiding to 1 to 3 feet. 
.sunday night...northwest winds 10 to 20 knots backing west late.
waves subsiding to calm to 2 feet. 
.monday...west winds 5 to 15 knots. waves calm to 2 feet. 
.monday night...southwest winds 5 to 15 knots becoming west 10 to
20 knots after midnight. waves calm to 2 feet. 
.tuesday...northwest winds 10 to 20 knots becoming northeast 5 to
15 knots by mid afternoon. waves calm to 2 feet. 
.tuesday night...south winds 5 to 15 knots. waves calm to 2 feet.
.wednesday...southeast winds 5 to 15 knots becoming south 10 to
20 knots. waves calm to 2 feet. 
.thursday...southwest winds 10 to 20 knots. a chance of showers
and thunderstorms. waves calm to 2 feet. 

$$

fzus63 kmqt 311945
glfls 
expires:202108010345;;764782

open lake forecast for lake superior
national weather service marquette mi
345 pm edt sat jul 31 2021

for waters beyond 5 nautical miles of shore on lake superior.

waves are the significant wave height - the average of the
highest 1/3 of the wave spectrum. occasional wave height is the
average of the highest 1/10 of the wave spectrum.

.synopsis...a 29.9 inch trough will push south out of the upper 
great lakes tonight. this trough will be followed by 30.1 inch 
ridging over lake superior sunday. this ridge will weaken slightly
to 30.0 inches monday night as a weak 29.9 inch trough clips the 
northern shore of the lake. the 30.0 inch ridging will persist 
through the remainder of the week while 29.8 inch troughing 
develops over northern minnesota. 


lsz266-010345-
lake superior east of a line from manitou island to marquette mi
and west of a line from grand marais mi to the us/canadian border
beyond 5nm from shore-
345 pm edt sat jul 31 2021

.late this afternoon...northwest winds 10 to 20 knots. patchy
smoke. waves calm to 2 feet building to 1 to 3 feet. 
.tonight...northwest winds 10 to 20 knots becoming north 15 to
25 knots after midnight. patchy smoke through midnight. isolated
showers after midnight. waves building to 3 to 5 feet
occasionally to 7 feet. 
.sunday...north winds 15 to 25 knots diminishing to 10 to
20 knots in the afternoon, then backing northwest late. waves
subsiding to 2 to 4 feet. 
.sunday night...northwest winds 10 to 20 knots. waves subsiding
to calm to 2 feet. 
.monday...west winds 5 to 15 knots increasing to 15 to 25 knots
by mid afternoon. waves building to 3 to 5 feet occasionally to
7 feet. 
.monday night...southwest winds 15 to 25 knots becoming west
10 to 20 knots after midnight. waves subsiding to calm to 2 feet.
.tuesday...northwest winds 10 to 20 knots diminishing to 5 to
15 knots by mid afternoon. waves calm to 2 feet. 
.tuesday night...west winds 5 to 15 knots backing south after
midnight. waves calm to 2 feet. 
.wednesday...south winds 5 to 15 knots increasing to 10 to
20 knots. waves building to 1 to 3 feet. 
.thursday...south winds 10 to 20 knots veering southwest. a
chance of showers and thunderstorms. waves 1 to 3 feet. 

$$

fzus63 kmqt 311945
glfls 
expires:202108010345;;764783

open lake forecast for lake superior
national weather service marquette mi
345 pm edt sat jul 31 2021

for waters beyond 5 nautical miles of shore on lake superior.

waves are the significant wave height - the average of the
highest 1/3 of the wave spectrum. occasional wave height is the
average of the highest 1/10 of the wave spectrum.

.synopsis...a 29.9 inch trough will push south out of the upper 
great lakes tonight. this trough will be followed by 30.1 inch 
ridging over lake superior sunday. this ridge will weaken slightly
to 30.0 inches monday night as a weak 29.9 inch trough clips the 
northern shore of the lake. the 30.0 inch ridging will persist 
through the remainder of the week while 29.8 inch troughing 
develops over northern minnesota. 


lsz267-010345-
lake superior from grand marais mi to whitefish point mi 5nm off
shore to the us/canadian border-
345 pm edt sat jul 31 2021

.late this afternoon...northwest winds 10 to 20 knots. patchy
smoke. waves calm to 2 feet. 
.tonight...northwest winds 10 to 20 knots veering north after
midnight, then increasing to 15 to 25 knots late. patchy smoke
through midnight. isolated showers. waves building to 3 to 5 feet
occasionally to 7 feet. 
.sunday...north winds 15 to 25 knots diminishing to 10 to
20 knots in the afternoon, then becoming northwest 15 to 25 knots
late. waves subsiding to 1 to 3 feet. 
.sunday night...northwest winds 10 to 20 knots diminishing to
5 to 15 knots late. waves building to 2 to 4 feet, then subsiding
to calm to 2 feet. 
.monday...west winds 5 to 15 knots increasing to 10 to 20 knots
by mid afternoon. waves calm to 2 feet. 
.monday night...southwest winds 10 to 20 knots veering west after
midnight. waves calm to 2 feet. 
.tuesday...northwest winds 10 to 20 knots. waves calm to 2 feet. 
.tuesday night...west winds 5 to 15 knots backing south after
midnight. waves calm to 2 feet. 
.wednesday...south winds 5 to 15 knots increasing to 10 to
20 knots. waves building to 1 to 3 feet. 
.thursday...south winds 10 to 20 knots. a chance of showers and
thunderstorms. waves 1 to 3 feet. 

$$

fzus63 kmqt 311945
glfls 
expires:202108010345;;764780

open lake forecast for lake superior
national weather service marquette mi
345 pm edt sat jul 31 2021

for waters beyond 5 nautical miles of shore on lake superior.

waves are the significant wave height - the average of the
highest 1/3 of the wave spectrum. occasional wave height is the
average of the highest 1/10 of the wave spectrum.

.synopsis...a 29.9 inch trough will push south out of the upper 
great lakes tonight. this trough will be followed by 30.1 inch 
ridging over lake superior sunday. this ridge will weaken slightly
to 30.0 inches monday night as a weak 29.9 inch trough clips the 
northern shore of the lake. the 30.0 inch ridging will persist 
through the remainder of the week while 29.8 inch troughing 
develops over northern minnesota. 


lsz264-010345-
lake superior from upper entrance to portage canal to manitou
island mi 5nm off shore to the us/canadian border-
345 pm edt sat jul 31 2021

.late this afternoon...northwest winds 5 to 15 knots. patchy
smoke. isolated showers and thunderstorms. waves calm to 2 feet
building to 1 to 3 feet. 
.tonight...north winds 10 to 20 knots. patchy smoke through
midnight. waves building to 2 to 4 feet. 
.sunday...north winds 10 to 20 knots diminishing to 5 to 15 knots
in the afternoon, then backing northwest late. waves subsiding to
calm to 2 feet. 
.sunday night...west winds 5 to 15 knots. waves calm to 2 feet. 
.monday...west winds 5 to 15 knots becoming southwest 15 to
25 knots by mid afternoon. waves building to 3 to 5 feet
occasionally to 7 feet. 
.monday night...west winds 15 to 25 knots diminishing to 10 to
20 knots after midnight. waves subsiding to calm to 2 feet. 
.tuesday...north winds 5 to 15 knots. waves calm to 2 feet. 
.tuesday night...southwest winds less than 10 knots backing south
after midnight. waves calm to 2 feet. 
.wednesday...south winds 5 to 15 knots. waves building to 1 to
3 feet. 
.thursday...southwest winds 5 to 15 knots. a chance of showers
and thunderstorms. waves 1 to 3 feet. 

$$

fzus63 kmqt 311945
glfls 
expires:202108010345;;764779

open lake forecast for lake superior
national weather service marquette mi
345 pm edt sat jul 31 2021

for waters beyond 5 nautical miles of shore on lake superior.

waves are the significant wave height - the average of the
highest 1/3 of the wave spectrum. occasional wave height is the
average of the highest 1/10 of the wave spectrum.

.synopsis...a 29.9 inch trough will push south out of the upper 
great lakes tonight. this trough will be followed by 30.1 inch 
ridging over lake superior sunday. this ridge will weaken slightly
to 30.0 inches monday night as a weak 29.9 inch trough clips the 
northern shore of the lake. the 30.0 inch ridging will persist 
through the remainder of the week while 29.8 inch troughing 
develops over northern minnesota. 


lsz263-010345-
lake superior from saxon harbor wi to upper entrance to portage
canal mi 5nm off shore to the us/canadian border including isle
royale national park-
345 pm edt sat jul 31 2021

.late this afternoon...west winds 10 to 20 knots. patchy smoke.
isolated showers and thunderstorms. waves calm to 2 feet. 
.tonight...northeast winds 10 to 20 knots becoming north 15 to
25 knots after midnight. patchy smoke through midnight. waves
building to 2 to 4 feet. 
.sunday...north winds 15 to 25 knots diminishing to 5 to 15 knots
in the afternoon, then backing southwest late. waves subsiding to
calm to 2 feet. 
.sunday night...southwest winds 5 to 15 knots increasing to 10 to
20 knots late. waves calm to 2 feet. 
.monday...west winds 10 to 20 knots backing southwest by mid
afternoon. waves building to 2 to 4 feet. 
.monday night...southwest winds 10 to 20 knots becoming west 5 to
15 knots after midnight. waves subsiding to calm to 2 feet. 
.tuesday...north winds 5 to 15 knots veering east by mid
afternoon. waves calm to 2 feet. 
.tuesday night...south winds 5 to 15 knots. waves calm to 2 feet.
.wednesday...south winds 5 to 15 knots increasing to 10 to
20 knots. waves building to 1 to 3 feet. 
.thursday...southwest winds 10 to 20 knots. a chance of showers
and thunderstorms. waves subsiding to calm to 2 feet. 

$$

fzus63 kmqt 311945
glfls 
expires:202108010345;;764778

open lake forecast for lake superior
national weather service marquette mi
345 pm edt sat jul 31 2021

for waters beyond 5 nautical miles of shore on lake superior.

waves are the significant wave height - the average of the
highest 1/3 of the wave spectrum. occasional wave height is the
average of the highest 1/10 of the wave spectrum.

.synopsis...a 29.9 inch trough will push south out of the upper 
great lakes tonight. this trough will be followed by 30.1 inch 
ridging over lake superior sunday. this ridge will weaken slightly
to 30.0 inches monday night as a weak 29.9 inch trough clips the 
northern shore of the lake. the 30.0 inch ridging will persist 
through the remainder of the week while 29.8 inch troughing 
develops over northern minnesota. 


lsz162-010345-
lake superior west of a line from saxon harbor wi to grand
portage mn beyond 5nm-
345 pm edt sat jul 31 2021 /245 pm cdt sat jul 31 2021/

.late this afternoon...west winds 10 to 20 knots. patchy smoke.
isolated showers and thunderstorms. waves calm to 2 feet. 
.tonight...north winds 10 to 20 knots. patchy smoke through
midnight. waves building to 1 to 3 feet. 
.sunday...north winds 10 to 20 knots becoming southeast 5 to
15 knots in the afternoon, then veering south late. waves
subsiding to calm to 2 feet. 
.sunday night...south winds 5 to 15 knots veering west late.
waves calm to 2 feet. 
.monday...west winds 5 to 15 knots becoming southwest 10 to
20 knots by mid afternoon. waves building to 1 to 3 feet. 
.monday night...west winds 10 to 20 knots diminishing to 5 to
15 knots after midnight. waves subsiding to calm to 2 feet. 
.tuesday...east winds 5 to 15 knots increasing to 10 to 20 knots
by mid afternoon. waves calm to 2 feet. 
.tuesday night...east winds 5 to 15 knots veering south after
midnight. waves calm to 2 feet. 
.wednesday...south winds 5 to 15 knots veering southwest. waves
calm to 2 feet. 
.thursday...southwest winds 10 to 20 knots. a chance of showers
and thunderstorms. waves building to 1 to 3 feet, then subsiding
to calm to 2 feet. 

$$