
162 
FNUS54 KMRX 160723
FWFMRX

FIRE WEATHER PLANNING FORECAST FOR EAST TENNESSEE...SOUTHWEST
VIRGINIA...AND EXTREME SOUTHWEST NORTH CAROLINA
NATIONAL WEATHER SERVICE MORRISTOWN TN
600 AM EDT SAT JUN 16 2012

.DISCUSSION...
HIGH PRESSURE WILL LINGER OVER THE SOUTHERN APPALACHIAN REGION 
THROUGH NEXT WEEK...WITH ISOLATED SHOWERS AND THUNDERSTORMS 
DEVELOPING EACH AFTERNOON AND EVENING...BUT MAINLY AROUND THE HIGHER 
ELEVATIONS. TEMPERATURES ARE EXPECTED TO BE SLIGHTLY ABOVE NORMAL 
THROUGH NEXT WEEK.


VAZ001-002-005-006-008-170815-
JEFFERSON NATIONAL FOREST/VIRGINIA DISTRICT 6-
600 AM EDT SAT JUN 16 2012

                      TODAY        TONIGHT      SUN          

CLOUD COVER           PCLDY        PCLDY        PCLDY        
TEMP (24H TREND)      80-85 (+1)   57-62 (0)    78-83        
RH % (24H TREND)      39-44 (-1)   86-91 (-1)   42-47        
20FT WIND-AM(MPH)     LGT/VAR                   SW  5        
20FT WIND-PM(MPH)     LGT/VAR      LGT/VAR      LGT/VAR      
PRECIP TYPE           TSTMS        TSTMS        TSTMS        
CHANCE PRECIP (%)     20           0            20           
PRECIP DURATION       1                         1            
PRECIP BEGIN          12 PM                     12 PM        
PRECIP END            CONTINUING                CONTINUING   
PRECIP AMOUNT         0.01         0.00         0.04         
LAL                   2            2            2            
LASI                  3                         3            
MIXING HGT(FT-MSL)    5900                      5900         
TRANSPORT WND (MPH)   E  6                      SW  8        
DISPERSION            19 GEN POOR               26 FAIR      

REMARKS...A FEW THUNDERSTORMS THIS AFTERNOON AND SUNDAY AFTERNOON 
MAY PRODUCE LOCALLY HEAVY RAINFALL UP TO AN INCH OR TWO.

.SUNDAY NIGHT...PARTLY CLOUDY. SLIGHT CHANCE OF SHOWERS AND 
THUNDERSTORMS. LOWS IN THE UPPER 50S TO MID 60S. SOUTH WINDS LESS 
THAN 10 MPH. 
.MONDAY...MOSTLY SUNNY. SLIGHT CHANCE OF SHOWERS AND THUNDERSTORMS. 
HIGHS IN THE 80S. SOUTHWEST WINDS LESS THAN 10 MPH. 
.MONDAY NIGHT...MOSTLY CLEAR. LOWS IN THE UPPER 50S TO MID 60S. SOUTH
WINDS LESS THAN 10 MPH. 
.TUESDAY...PARTLY CLOUDY. SLIGHT CHANCE OF SHOWERS AND 
THUNDERSTORMS. HIGHS IN THE 80S. SOUTHEAST WINDS LESS THAN 10 MPH. 
.WEDNESDAY...PARTLY CLOUDY. SLIGHT CHANCE OF SHOWERS AND 
THUNDERSTORMS. LOWS IN THE MID 60S. HIGHS IN THE MID 80S TO LOWER 
90S. SOUTHEAST WINDS LESS THAN 10 MPH. 
.THURSDAY...PARTLY CLOUDY. SLIGHT CHANCE OF SHOWERS AND 
THUNDERSTORMS. LOWS IN THE MID 60S. HIGHS IN THE 80S. SOUTH WINDS 
LESS THAN 10 MPH. 
.FRIDAY...PARTLY CLOUDY. SLIGHT CHANCE OF SHOWERS AND THUNDERSTORMS. 
LOWS IN THE MID 60S. HIGHS IN THE 80S. SOUTHWEST WINDS LESS THAN 10 
MPH. 

$$

TNZ018-041-043-045-047-170815-
NORTHERN CHEROKEE NATIONAL FOREST-
600 AM EDT SAT JUN 16 2012

                      TODAY        TONIGHT      SUN          

CLOUD COVER           PCLDY        PCLDY        PCLDY        
TEMP (24H TREND)      73-78 (+1)   56-61 (0)    76-81        
RH % (24H TREND)      46-51 (+6)   87-92 (0)    41-46        
20FT WIND-AM(MPH)     LGT/VAR                   LGT/VAR      
20FT WIND-PM(MPH)     LGT/VAR      SE  5        LGT/VAR      
PRECIP TYPE           TSTMS        TSTMS        TSTMS        
CHANCE PRECIP (%)     20           20           20           
PRECIP DURATION       1            1            1            
PRECIP BEGIN          12 PM        CONTINUING   12 PM        
PRECIP END            CONTINUING   12 AM        CONTINUING   
PRECIP AMOUNT         0.02         0.01         0.04         
LAL                   2            2            2            
LASI                  3                         3            
MIXING HGT(FT-MSL)    5400                      5900         
TRANSPORT WND (MPH)   NE  6                     W  6         
DISPERSION            13 GEN POOR               16 GEN POOR  

REMARKS...A FEW THUNDERSTORMS THROUGH SUNDAY AFTERNOON MAY PRODUCE 
LOCALLY HEAVY RAINFALL UP TO AN INCH OR TWO.

.SUNDAY NIGHT...PARTLY CLOUDY. SLIGHT CHANCE OF SHOWERS AND 
THUNDERSTORMS. LOWS IN THE MID 50S TO LOWER 60S. SOUTHWEST WINDS 
LESS THAN 10 MPH. 
.MONDAY...MOSTLY SUNNY. SLIGHT CHANCE OF SHOWERS AND THUNDERSTORMS. 
HIGHS IN THE 80S. SOUTHWEST WINDS LESS THAN 10 MPH. 
.MONDAY NIGHT...MOSTLY CLEAR. LOWS IN THE MID 50S TO LOWER 60S. 
SOUTH WINDS LESS THAN 10 MPH. 
.TUESDAY...PARTLY CLOUDY. SLIGHT CHANCE OF SHOWERS AND 
THUNDERSTORMS. HIGHS IN THE 80S. NORTH WINDS LESS THAN 10 MPH. 
.WEDNESDAY...PARTLY CLOUDY. SLIGHT CHANCE OF SHOWERS AND 
THUNDERSTORMS. LOWS IN THE LOWER 60S. HIGHS IN THE MID 80S TO LOWER 
90S. WEST WINDS LESS THAN 10 MPH. 
.THURSDAY...PARTLY CLOUDY. SLIGHT CHANCE OF SHOWERS AND 
THUNDERSTORMS. LOWS IN THE LOWER 60S. HIGHS IN THE 80S. NORTHWEST 
WINDS LESS THAN 10 MPH. 
.FRIDAY...PARTLY CLOUDY. SLIGHT CHANCE OF SHOWERS AND THUNDERSTORMS. 
LOWS IN THE MID 60S. HIGHS IN THE 80S. WEST WINDS LESS THAN 10 MPH. 

$$

TNZ072-074-170815-
TENNESSEE PORTION OF THE GREAT SMOKY MOUNTAIN NATIONAL PARK-
600 AM EDT SAT JUN 16 2012

                      TODAY        TONIGHT      SUN          

CLOUD COVER           PCLDY        PCLDY        PCLDY        
TEMP (24H TREND)      72-77 (+1)   56-61 (0)    77-82        
RH % (24H TREND)      45-50 (+1)   87-92 (0)    37-42        
20FT WIND-AM(MPH)     LGT/VAR                   LGT/VAR      
20FT WIND-PM(MPH)     NE  5        LGT/VAR      LGT/VAR      
PRECIP TYPE           TSTMS        TSTMS        TSTMS        
CHANCE PRECIP (%)     20           20           20           
PRECIP DURATION       1            1            1            
PRECIP BEGIN          12 PM        CONTINUING   12 PM        
PRECIP END            CONTINUING   12 AM        CONTINUING   
PRECIP AMOUNT         0.02         0.01         0.04         
LAL                   2            2            2            
LASI                  3                         3            
MIXING HGT(FT-MSL)    5400                      5900         
TRANSPORT WND (MPH)   NE  7                     W  6         
DISPERSION            13 GEN POOR               15 GEN POOR  

REMARKS...A FEW THUNDERSTORMS THROUGH SUNDAY AFTERNOON MAY PRODUCE 
LOCALLY HEAVY RAINFALL UP TO AN INCH OR TWO.

.SUNDAY NIGHT...PARTLY CLOUDY. SLIGHT CHANCE OF SHOWERS AND 
THUNDERSTORMS. LOWS IN THE LOWER 50S TO MID 60S. SOUTH WINDS LESS 
THAN 10 MPH. 
.MONDAY...MOSTLY SUNNY. SLIGHT CHANCE OF SHOWERS AND THUNDERSTORMS. 
HIGHS IN THE LOWER 70S TO MID 80S. WEST WINDS LESS THAN 10 MPH. 
.MONDAY NIGHT...MOSTLY CLEAR. LOWS IN THE MID 50S TO MID 60S. SOUTH 
WINDS LESS THAN 10 MPH. 
.TUESDAY...PARTLY CLOUDY. SLIGHT CHANCE OF SHOWERS AND 
THUNDERSTORMS. HIGHS IN THE MID 70S TO UPPER 80S. SOUTHWEST WINDS 
LESS THAN 10 MPH. 
.WEDNESDAY...PARTLY CLOUDY. SLIGHT CHANCE OF SHOWERS AND 
THUNDERSTORMS. LOWS IN THE 60S. HIGHS IN THE MID 70S TO UPPER 80S. 
SOUTHWEST WINDS LESS THAN 10 MPH. 
.THURSDAY...PARTLY CLOUDY. SLIGHT CHANCE OF SHOWERS AND 
THUNDERSTORMS. LOWS IN THE 60S. HIGHS IN THE MID 70S TO UPPER 80S. 
WEST WINDS LESS THAN 10 MPH. 
.FRIDAY...PARTLY CLOUDY. SLIGHT CHANCE OF SHOWERS AND THUNDERSTORMS. 
LOWS IN THE 60S. HIGHS IN THE MID 70S TO UPPER 80S. SOUTHWEST WINDS 
LESS THAN 10 MPH. 

$$

TNZ087-102-170815-
SOUTHERN CHEROKEE NATIONAL FOREST-
600 AM EDT SAT JUN 16 2012

                      TODAY        TONIGHT      SUN          

CLOUD COVER           PCLDY        PCLDY        PCLDY        
TEMP (24H TREND)      76-81 (+1)   58-63 (0)    82-87        
RH % (24H TREND)      42-47 (-3)   87-92 (-2)   36-41        
20FT WIND-AM(MPH)     LGT/VAR                   LGT/VAR      
20FT WIND-PM(MPH)     LGT/VAR      LGT/VAR      LGT/VAR      
PRECIP TYPE           TSTMS        TSTMS        NONE         
CHANCE PRECIP (%)     20           20           0            
PRECIP DURATION       1            1                         
PRECIP BEGIN          12 PM        CONTINUING                
PRECIP END            CONTINUING   12 AM                     
PRECIP AMOUNT         0.02         0.01         0.00         
LAL                   2            2            1            
LASI                  3                         4            
MIXING HGT(FT-MSL)    5100                      6000         
TRANSPORT WND (MPH)   E  6                      SW  7        
DISPERSION            15 GEN POOR               22 FAIR      

REMARKS...A FEW THUNDERSTORMS THIS AFTERNOON AND EVENING MAY PRODUCE 
LOCALLY HEAVY RAINFALL UP TO AN INCH OR TWO.

.SUNDAY NIGHT...PARTLY CLOUDY. LOWS IN THE UPPER 50S TO MID 60S. 
SOUTH WINDS LESS THAN 10 MPH. 
.MONDAY...MOSTLY SUNNY. SLIGHT CHANCE OF SHOWERS AND THUNDERSTORMS. 
HIGHS IN THE 80S. SOUTHWEST WINDS LESS THAN 10 MPH. 
.MONDAY NIGHT...MOSTLY CLEAR. LOWS IN THE UPPER 50S TO MID 60S. 
SOUTH WINDS LESS THAN 10 MPH. 
.TUESDAY...PARTLY CLOUDY. SLIGHT CHANCE OF SHOWERS AND 
THUNDERSTORMS. HIGHS IN THE 80S. EAST WINDS LESS THAN 10 MPH. 
.WEDNESDAY...PARTLY CLOUDY. SLIGHT CHANCE OF SHOWERS AND 
THUNDERSTORMS. LOWS IN THE LOWER 60S. HIGHS IN THE MID 80S TO LOWER 
90S. SOUTHWEST WINDS LESS THAN 10 MPH. 
.THURSDAY...PARTLY CLOUDY. SLIGHT CHANCE OF SHOWERS AND 
THUNDERSTORMS. LOWS IN THE MID 60S. HIGHS IN THE 80S. WEST WINDS 
LESS THAN 10 MPH. 
.FRIDAY...PARTLY CLOUDY. SLIGHT CHANCE OF SHOWERS AND THUNDERSTORMS. 
LOWS IN THE UPPER 60S. HIGHS IN THE 80S. SOUTHWEST WINDS LESS THAN 
10 MPH. 

$$

NCZ060-061-170815-
NANTAHALA NATIONAL FOREST-
600 AM EDT SAT JUN 16 2012

                      TODAY        TONIGHT      SUN          

CLOUD COVER           PCLDY        PCLDY        PCLDY        
TEMP (24H TREND)      75-80 (+1)   57-62 (0)    81-86        
RH % (24H TREND)      42-47 (-3)   88-93 (-2)   35-40        
20FT WIND-AM(MPH)     LGT/VAR                   LGT/VAR      
20FT WIND-PM(MPH)     LGT/VAR      LGT/VAR      LGT/VAR      
PRECIP TYPE           TSTMS        TSTMS        NONE         
CHANCE PRECIP (%)     20           20           0            
PRECIP DURATION       1            1                         
PRECIP BEGIN          12 PM        CONTINUING                
PRECIP END            CONTINUING   12 AM                     
PRECIP AMOUNT         0.02         0.01         0.00         
LAL                   2            2            1            
LASI                  3                         3            
MIXING HGT(FT-MSL)    5600                      6000         
TRANSPORT WND (MPH)   E  6                      SW  6        
DISPERSION            17 GEN POOR               19 GEN POOR  
MAX LVORI             4                         3            

REMARKS...A FEW THUNDERSTORMS THIS AFTERNOON AND EVENING MAY PRODUCE 
LOCALLY HEAVY RAINFALL UP TO AN INCH OR TWO.

.SUNDAY NIGHT...PARTLY CLOUDY. LOWS IN THE UPPER 50S TO MID 60S. 
SOUTH WINDS LESS THAN 10 MPH.
.MONDAY...MOSTLY SUNNY. SLIGHT CHANCE OF SHOWERS AND THUNDERSTORMS. 
HIGHS IN THE 80S. SOUTHWEST WINDS LESS THAN 10 MPH. 
.MONDAY NIGHT...MOSTLY CLEAR. LOWS NEAR 60. SOUTHEAST WINDS LESS 
THAN 10 MPH. 
.TUESDAY...PARTLY CLOUDY. SLIGHT CHANCE OF SHOWERS AND 
THUNDERSTORMS. HIGHS IN THE 80S. NORTHEAST WINDS LESS THAN 10 MPH. 
.WEDNESDAY...PARTLY CLOUDY. SLIGHT CHANCE OF SHOWERS AND 
THUNDERSTORMS. LOWS IN THE LOWER 60S. HIGHS IN THE 80S. NORTHEAST 
WINDS LESS THAN 10 MPH. 
.THURSDAY...PARTLY CLOUDY. SLIGHT CHANCE OF SHOWERS AND 
THUNDERSTORMS. LOWS IN THE MID 60S. HIGHS IN THE 80S. NORTHWEST 
WINDS LESS THAN 10 MPH. 
.FRIDAY...PARTLY CLOUDY. SLIGHT CHANCE OF SHOWERS AND THUNDERSTORMS. 
LOWS IN THE UPPER 60S. HIGHS IN THE 80S. NORTHWEST WINDS LESS THAN 
10 MPH. 

$$

TNZ015>017-038>040-042-044-046-070-170815-
EAST TENNESSEE DISTRICT EAST-
600 AM EDT SAT JUN 16 2012

                      TODAY        TONIGHT      SUN          

CLOUD COVER           PCLDY        PCLDY        PCLDY        
TEMP (24H TREND)      82-87 (+1)   58-63 (0)    81-86        
RH % (24H TREND)      38-43 (-2)   84-89 (-3)   38-43        
20FT WIND-AM(MPH)     LGT/VAR                   LGT/VAR      
20FT WIND-PM(MPH)     LGT/VAR      LGT/VAR      LGT/VAR      
PRECIP TYPE           NONE         NONE         TSTMS        
CHANCE PRECIP (%)     0            0            20           
PRECIP DURATION                                 1            
PRECIP BEGIN                                    12 PM        
PRECIP END                                      CONTINUING   
PRECIP AMOUNT         0.00         0.00         0.03         
LAL                   1            1            2            
LASI                  3                         3            
MIXING HGT(FT-MSL)    5600                      5600         
TRANSPORT WND (MPH)   E  6                      SW  7        
DISPERSION            21 FAIR                   25 FAIR      

REMARKS...A FEW THUNDERSTORMS ON SUNDAY AFTERNOON MAY PRODUCE 
LOCALLY HEAVY RAINFALL UP TO AN INCH OR TWO.

.SUNDAY NIGHT...PARTLY CLOUDY. SLIGHT CHANCE OF SHOWERS AND 
THUNDERSTORMS. LOWS IN THE UPPER 50S TO MID 60S. SOUTH WINDS LESS 
THAN 10 MPH. 
.MONDAY...MOSTLY SUNNY. HIGHS IN THE 80S. SOUTHWEST WINDS LESS THAN 
10 MPH. 
.MONDAY NIGHT...MOSTLY CLEAR. LOWS IN THE UPPER 50S TO MID 60S. 
SOUTH WINDS LESS THAN 10 MPH. 
.TUESDAY...PARTLY CLOUDY. HIGHS IN THE MID 80S TO LOWER 90S. EAST 
WINDS LESS THAN 10 MPH. 
.WEDNESDAY...PARTLY CLOUDY. SLIGHT CHANCE OF SHOWERS AND 
THUNDERSTORMS. LOWS IN THE MID 60S. HIGHS IN THE MID 80S TO LOWER 
90S. SOUTH WINDS LESS THAN 10 MPH. 
.THURSDAY...PARTLY CLOUDY. SLIGHT CHANCE OF SHOWERS AND 
THUNDERSTORMS. LOWS IN THE MID 60S. HIGHS IN THE MID 80S TO LOWER 
90S. SOUTHWEST WINDS LESS THAN 10 MPH. 
.FRIDAY...PARTLY CLOUDY. SLIGHT CHANCE OF SHOWERS AND THUNDERSTORMS. 
LOWS IN THE MID 60S. HIGHS IN THE 80S. SOUTHWEST WINDS LESS THAN 10 
MPH. 

$$

TNZ012>014-035>037-067>069-071-073-086-170815-
EAST TENNESSEE DISTRICT WEST-
600 AM EDT SAT JUN 16 2012

                      TODAY        TONIGHT      SUN          

CLOUD COVER           PCLDY        PCLDY        PCLDY        
TEMP (24H TREND)      83-88 (+1)   60-65 (0)    82-87        
RH % (24H TREND)      37-42 (-5)   84-89 (-5)   36-41        
20FT WIND-AM(MPH)     LGT/VAR                   SW  6        
20FT WIND-PM(MPH)     LGT/VAR      LGT/VAR      SW  5        
PRECIP TYPE           TSTMS        NONE         TSTMS        
CHANCE PRECIP (%)     10           0            20           
PRECIP DURATION       1                         1            
PRECIP BEGIN          12 PM                     12 PM        
PRECIP END            CONTINUING                CONTINUING   
PRECIP AMOUNT         0.01         0.00         0.02         
LAL                   1            1            2            
LASI                  3                         3            
MIXING HGT(FT-MSL)    5500                      5700         
TRANSPORT WND (MPH)   S  6                      SW 10        
DISPERSION            21 FAIR                   40 FAIR      

REMARKS...A FEW THUNDERSTORMS THIS AFTERNOON AND SUNDAY AFTERNOON 
MAY PRODUCE LOCALLY HEAVY RAINFALL UP TO AN INCH OR TWO.

.SUNDAY NIGHT...PARTLY CLOUDY. SLIGHT CHANCE OF SHOWERS AND 
THUNDERSTORMS. LOWS IN THE LOWER TO MID 60S. SOUTHWEST WINDS LESS 
THAN 10 MPH. 
.MONDAY...MOSTLY SUNNY. HIGHS IN THE MID 80S TO LOWER 90S. SOUTHWEST 
WINDS LESS THAN 10 MPH. 
.MONDAY NIGHT...MOSTLY CLEAR. LOWS IN THE 60S. SOUTH WINDS LESS THAN 
10 MPH. 
.TUESDAY...PARTLY CLOUDY. HIGHS IN THE MID 80S TO LOWER 90S. WEST 
WINDS LESS THAN 10 MPH. 
.WEDNESDAY...PARTLY CLOUDY. SLIGHT CHANCE OF SHOWERS AND 
THUNDERSTORMS. LOWS IN THE MID 60S. HIGHS IN THE MID 80S TO LOWER 
90S. WEST WINDS LESS THAN 10 MPH. 
.THURSDAY...PARTLY CLOUDY. SLIGHT CHANCE OF SHOWERS AND 
THUNDERSTORMS. LOWS IN THE UPPER 60S. HIGHS IN THE MID 80S TO LOWER 
90S. WEST WINDS LESS THAN 10 MPH. 
.FRIDAY...PARTLY CLOUDY. SLIGHT CHANCE OF SHOWERS AND THUNDERSTORMS. 
LOWS IN THE UPPER 60S. HIGHS IN THE 80S. SOUTHWEST WINDS LESS THAN 
10 MPH. 

$$

TNZ076-077-079>085-097>101-170815-
CUMBERLAND DISTRICT SOUTH-
600 AM EDT SAT JUN 16 2012 /500 AM CDT SAT JUN 16 2012/

                      TODAY        TONIGHT      SUN          

CLOUD COVER           PCLDY        PCLDY        PCLDY        
TEMP (24H TREND)      81-86 (+1)   60-65 (0)    83-88        
RH % (24H TREND)      40-45 (-4)   84-89 (-4)   34-39        
20FT WIND-AM(MPH)     S  5                      S  6         
20FT WIND-PM(MPH)     LGT/VAR      LGT/VAR      S  6         
PRECIP TYPE           TSTMS        NONE         NONE         
CHANCE PRECIP (%)     10           0            0            
PRECIP DURATION       1                                      
PRECIP BEGIN          12 PM                                  
PRECIP END            CONTINUING                             
PRECIP AMOUNT         0.01         0.00         0.00         
LAL                   1            1            1            
LASI                  3                         4            
MIXING HGT(FT-MSL)    5100                      5700         
TRANSPORT WND (MPH)   SE  6                     SW  9        
DISPERSION            20 GEN POOR               37 FAIR      

REMARKS...NONE.

.SUNDAY NIGHT...PARTLY CLOUDY. LOWS IN THE MID 60S. SOUTH WINDS LESS 
THAN 10 MPH. 
.MONDAY...MOSTLY SUNNY. HIGHS IN THE MID 80S TO LOWER 90S. SOUTH
WINDS UP TO 10 MPH. 
.MONDAY NIGHT...MOSTLY CLEAR. LOWS IN THE 60S. SOUTH WINDS LESS
THAN 10 MPH. 
.TUESDAY...PARTLY CLOUDY. HIGHS IN THE MID 80S TO LOWER 90S. 
SOUTHEAST WINDS LESS THAN 10 MPH. 
.WEDNESDAY...PARTLY CLOUDY. SLIGHT CHANCE OF SHOWERS AND 
THUNDERSTORMS. LOWS IN THE UPPER 60S. HIGHS IN THE MID 80S TO LOWER 
90S. SOUTHEAST WINDS LESS THAN 10 MPH. 
.THURSDAY...PARTLY CLOUDY. SLIGHT CHANCE OF SHOWERS AND 
THUNDERSTORMS. LOWS IN THE UPPER 60S. HIGHS IN THE MID 80S TO LOWER 
90S. EAST WINDS LESS THAN 10 MPH. 
.FRIDAY...PARTLY CLOUDY. SLIGHT CHANCE OF SHOWERS AND THUNDERSTORMS. 
LOWS IN THE UPPER 60S. HIGHS IN THE MID 80S TO LOWER 90S. SOUTH 
WINDS LESS THAN 10 MPH. 

$$

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