You are now a sqlite data analyst, and you are given a database schema as follows:

    【Schema】
    【DB_ID】 hockey
【Schema】
# Table: Scoring
[
(playerID:TEXT, Examples: [aaltoan01, abbeybr01, abbotge01]),
(year:INTEGER, Examples: [1997, 1998, 1999]),
(stint:INTEGER, Examples: [1, 2, 3]),
(tmID:TEXT, Examples: [ANA, CIN, BOS]),
(lgID:TEXT, Examples: [NHL, WHA, PCHA]),
(pos:TEXT, Examples: [C, D, G]),
(GP:INTEGER, Examples: [3, 73, 63]),
(G:INTEGER, Examples: [0, 3, 7]),
(A:INTEGER, Examples: [0, 5, 11]),
(Pts:INTEGER, Examples: [0, 8, 18]),
(PIM:INTEGER, Examples: [0, 24, 26]),
(+/-:TEXT, Examples: [-1, -12, -13]),
(PPG:TEXT, Examples: [0, 2, 1]),
(PPA:TEXT, Examples: [0, 1, 2]),
(SHG:TEXT, Examples: [0, 2, 1]),
(SHA:TEXT, Examples: [0, 1, 2]),
(GWG:TEXT, Examples: [0, 1, 3]),
(GTG:TEXT, Examples: [0, 1, 3]),
(SOG:TEXT, Examples: [1, 61, 102]),
(PostGP:TEXT, Examples: [4, 10, 11]),
(PostG:TEXT, Examples: [0, 2, 1]),
(PostA:TEXT, Examples: [0, 1, 3]),
(PostPts:TEXT, Examples: [0, 3, 2]),
(PostPIM:TEXT, Examples: [2, 0, 36]),
(Post+/-:TEXT, Examples: [0, 2, 1]),
(PostPPG:TEXT, Examples: [0, 1, 5]),
(PostPPA:TEXT, Examples: [0, 1, 3]),
(PostSHG:TEXT, Examples: [0, 1, 2]),
(PostSHA:TEXT, Examples: [0, 1, 2]),
(PostGWG:TEXT, Examples: [0, 1, 2]),
(PostSOG:TEXT, Examples: [0, 11, 12])
]
# Table: SeriesPost
[
(year:INTEGER, Examples: [1912, 1913, 1914]),
(round:TEXT, Examples: [SCF, F, SF]),
(series:TEXT, Examples: [A, B, C]),
(tmIDWinner:TEXT, Examples: [VA1, TBS, OT1]),
(lgIDWinner:TEXT, Examples: [PCHA, NHA, NHL]),
(tmIDLoser:TEXT, Examples: [QU1, MOC, VA1]),
(lgIDLoser:TEXT, Examples: [NHA, PCHA, NHL]),
(W:INTEGER, Examples: [2, 1, 3]),
(L:INTEGER, Examples: [1, 0, 2]),
(T:INTEGER, Examples: [0, 1, 2]),
(GoalsWinner:INTEGER, Examples: [16, 6, 13]),
(GoalsLoser:INTEGER, Examples: [12, 2, 8]),
(note:TEXT, Examples: [EX, TG, ND])
]
# Table: TeamsPost
[
(year:INTEGER, Primary Key, Examples: [1913, 1914, 1916]),
(lgID:TEXT, Examples: [NHA, NHL, PCHA]),
(tmID:TEXT, Primary Key, Examples: [MOC, TBS, MOW]),
(G:INTEGER, Examples: [2, 5, 6]),
(W:INTEGER, Examples: [1, 0, 4]),
(L:INTEGER, Examples: [1, 0, 4]),
(T:INTEGER, Examples: [0, 1, 2]),
(GF:INTEGER, Examples: [2, 6, 1]),
(GA:INTEGER, Examples: [6, 2, 4]),
(PIM:TEXT, Examples: [59, 68, 87]),
(BenchMinor:TEXT, Examples: [0, 6, 2]),
(PPG:TEXT, Examples: [1, 5, 9]),
(PPC:TEXT, Examples: [39, 27, 25]),
(SHA:TEXT, Examples: [0, 1, 2]),
(PKG:TEXT, Examples: [3, 8, 4]),
(PKC:TEXT, Examples: [55, 45, 20]),
(SHF:TEXT, Examples: [0, 1, 3])
]
# Table: ScoringShootout
[
(playerID:TEXT, Examples: [adamske01, afanadm01, afinoma01]),
(year:INTEGER, Examples: [2006, 2005, 2007]),
(stint:INTEGER, Examples: [1, 2, 3]),
(tmID:TEXT, Examples: [PHO, TBL, BUF]),
(S:INTEGER, Examples: [1, 2, 5]),
(G:INTEGER, Examples: [0, 1, 3]),
(GDG:INTEGER, Examples: [0, 1, 2])
]
# Table: AwardsCoaches
[
(coachID:TEXT, Examples: [patrile01c, irvindi01c, gormato01c]),
(award:TEXT, Examples: [First Team All-Star, Second Team All-Star, Jack Adams]),
(year:INTEGER, Examples: [1930, 1931, 1932]),
(lgID:TEXT, Examples: [NHL, WHA]),
(note:TEXT)
]
# Table: AwardsMisc
[
(name:TEXT, Primary Key, Examples: [1960 U.S. Olympic Hockey Team]),
(ID:TEXT, Examples: [arboual01, delveal01, rossar01]),
(award:TEXT, Examples: [Patrick]),
(year:INTEGER, Examples: [2001, 1998, 1991]),
(lgID:TEXT, Examples: [NHL]),
(note:TEXT, Examples: [posthumous])
]
# Table: Master
[
(playerID:TEXT, Examples: [aaltoan01, abbeybr01, abbotge01]),
(coachID:TEXT, Examples: [abelsi01c, adamsja01c, agnewga01c]),
(hofID:TEXT, Examples: [abelsi01h, adamsch01h, adamsja01h]),
(firstName:TEXT, Examples: [Antti, Bruce, George]),
(lastName:TEXT, Examples: [Aalto, Abbey, Abbott]),
(nameNote:TEXT, Examples: [also known as Bellehumeur]),
(nameGiven:TEXT, Examples: [Antti, Bruce, George Henry]),
(nameNick:TEXT, Examples: [Preacher, Taffy, Boot Nose]),
(height:TEXT, Examples: [73, 67, 71]),
(weight:TEXT, Examples: [210, 185, 153]),
(shootCatch:TEXT, Examples: [L, R, B]),
(legendsID:TEXT, Examples: [14862, 18411, 11801]),
(ihdbID:TEXT, Examples: [5928, 11918, 14591]),
(hrefID:TEXT, Examples: [aaltoan01, abbeybr01, abbotge01]),
(firstNHL:TEXT, Examples: [1997, 1943, 1952]),
(lastNHL:TEXT, Examples: [2000, 1943, 1952]),
(firstWHA:TEXT, Examples: [1975, 1976, 1974]),
(lastWHA:TEXT, Examples: [1975, 1977, 1976]),
(pos:TEXT, Examples: [C, D, G]),
(birthYear:TEXT, Examples: [1975, 1951, 1911]),
(birthMon:TEXT, Examples: [3, 8, 2]),
(birthDay:TEXT, Examples: [4, 18, 3]),
(birthCountry:TEXT, Examples: [Finland, Canada, USA]),
(birthState:TEXT, Examples: [ON, MB, MI]),
(birthCity:TEXT, Examples: [Lappeenranta, Toronto, Synenham]),
(deathYear:TEXT, Examples: [1964, 2000, 2001]),
(deathMon:TEXT, Examples: [8, 2, 12]),
(deathDay:TEXT, Examples: [1, 7, 24]),
(deathCountry:TEXT, Examples: [USA, Canada, France]),
(deathState:TEXT, Examples: [MI, AB, SK]),
(deathCity:TEXT, Examples: [Sault Ste. Marie, Farmington, Calgary])
]
# Table: ScoringSC
[
(playerID:TEXT, Examples: [adamsbi01, adamsja01, anderer02]),
(year:INTEGER, Examples: [1920, 1921, 1923]),
(tmID:TEXT, Examples: [VML, CAT, VIC]),
(lgID:TEXT, Examples: [PCHA, WCHL, NHL]),
(pos:TEXT, Examples: [R, C, L]),
(GP:INTEGER, Examples: [4, 5, 2]),
(G:INTEGER, Examples: [0, 2, 6]),
(A:INTEGER, Examples: [0, 1, 2]),
(Pts:INTEGER, Examples: [0, 3, 7]),
(PIM:INTEGER, Examples: [0, 6, 18])
]
# Table: TeamsSC
[
(year:INTEGER, Primary Key, Examples: [1912, 1913, 1914]),
(lgID:TEXT, Examples: [NHA, PCHA, NHL]),
(tmID:TEXT, Primary Key, Examples: [QU1, VA1, TBS]),
(G:INTEGER, Examples: [3, 5, 4]),
(W:INTEGER, Examples: [1, 2, 3]),
(L:INTEGER, Examples: [2, 1, 0]),
(T:INTEGER, Examples: [0, 1]),
(GF:INTEGER, Examples: [12, 16, 13]),
(GA:INTEGER, Examples: [16, 12, 8]),
(PIM:TEXT, Examples: [24, 20, 75])
]
# Table: TeamSplits
[
(year:INTEGER, Primary Key, Examples: [1909, 1910, 1911]),
(lgID:TEXT, Examples: [NHA, PCHA, NHL]),
(tmID:TEXT, Primary Key, Examples: [COB, HAI, LES]),
(hW:INTEGER, Examples: [2, 3, 6]),
(hL:INTEGER, Examples: [4, 3, 2]),
(hT:INTEGER, Examples: [0, 1, 2]),
(hOTL:TEXT, Examples: [2, 3, 1]),
(rW:INTEGER, Examples: [2, 1, 0]),
(rL:INTEGER, Examples: [4, 5, 6]),
(rT:INTEGER, Examples: [0, 1, 2]),
(rOTL:TEXT, Examples: [1, 5, 3]),
(SepW:TEXT, Examples: [1]),
(SepL:TEXT, Examples: [1]),
(SepT:TEXT),
(SepOL:TEXT, Examples: [0]),
(OctW:TEXT, Examples: [0, 1, 2]),
(OctL:TEXT, Examples: [1, 0, 2]),
(OctT:TEXT, Examples: [0, 1, 4]),
(OctOL:TEXT, Examples: [1, 0, 2]),
(NovW:TEXT, Examples: [5, 1, 2]),
(NovL:TEXT, Examples: [1, 4, 3]),
(NovT:TEXT, Examples: [0, 1, 2]),
(NovOL:TEXT, Examples: [0, 2, 1]),
(DecW:TEXT, Examples: [0, 1, 2]),
(DecL:TEXT, Examples: [1, 0, 2]),
(DecT:TEXT, Examples: [0, 1, 2]),
(DecOL:TEXT, Examples: [0, 2, 1]),
(JanW:INTEGER, Examples: [1, 0, 2]),
(JanL:INTEGER, Examples: [1, 3, 2]),
(JanT:INTEGER, Examples: [0, 1, 3]),
(JanOL:TEXT, Examples: [0, 1, 2]),
(FebW:INTEGER, Examples: [2, 1, 6]),
(FebL:INTEGER, Examples: [3, 5, 0]),
(FebT:INTEGER, Examples: [0, 1, 2]),
(FebOL:TEXT, Examples: [0, 1, 4]),
(MarW:TEXT, Examples: [1, 3, 0]),
(MarL:TEXT, Examples: [4, 0, 2]),
(MarT:TEXT, Examples: [0, 1, 2]),
(MarOL:TEXT, Examples: [1, 0, 2]),
(AprW:TEXT, Examples: [1, 0, 2]),
(AprL:TEXT, Examples: [0, 2, 1]),
(AprT:TEXT, Examples: [0, 1, 2]),
(AprOL:TEXT, Examples: [1, 0, 2])
]
# Table: GoaliesSC
[
(playerID:TEXT, Primary Key, Examples: [benedcl01, clancki01, holmeha01]),
(year:INTEGER, Primary Key, Examples: [1914, 1919, 1920]),
(tmID:TEXT, Examples: [OT1, OTS, MTM]),
(lgID:TEXT, Examples: [NHA, NHL, PCHA]),
(GP:INTEGER, Examples: [3, 5, 6]),
(Min:INTEGER, Examples: [180, 300, 361]),
(W:INTEGER, Examples: [0, 3, 5]),
(L:INTEGER, Examples: [3, 2, 1]),
(T:INTEGER, Examples: [0, 1]),
(SHO:INTEGER, Examples: [0, 1, 3]),
(GA:INTEGER, Examples: [26, 11, 12])
]
# Table: CombinedShutouts
[
(year:INTEGER, Examples: [1929, 1941, 1955]),
(month:INTEGER, Examples: [3, 2, 11]),
(date:INTEGER, Examples: [14, 15, 22]),
(tmID:TEXT, Examples: [TOR, MTL, OAK]),
(oppID:TEXT, Examples: [NYA, BOS, PHI]),
(R/P:TEXT, Examples: [R, P]),
(IDgoalie1:TEXT, Examples: [chabolo01, bibeapa01, plantja01]),
(IDgoalie2:TEXT, Examples: [grantbe01, gardibe01, hodgech01])
]
# Table: GoaliesShootout
[
(playerID:TEXT, Examples: [aebisda01, andercr01, aubinje01]),
(year:INTEGER, Examples: [2005, 2006, 2008]),
(stint:INTEGER, Examples: [1, 2]),
(tmID:TEXT, Examples: [COL, MTL, CHI]),
(W:INTEGER, Examples: [2, 0, 1]),
(L:INTEGER, Examples: [1, 2, 3]),
(SA:INTEGER, Examples: [10, 18, 7]),
(GA:INTEGER, Examples: [2, 6, 5])
]
# Table: Teams
[
(year:INTEGER, Primary Key, Examples: [1909, 1910, 1911]),
(lgID:TEXT, Examples: [NHA, PCHA, NHL]),
(tmID:TEXT, Primary Key, Examples: [COB, HAI, LES]),
(franchID:TEXT, Examples: [BKN, MTL, TBS]),
(confID:TEXT, Examples: [CC, WA, WC]),
(divID:TEXT, Examples: [AM, CA, ED]),
(rank:INTEGER, Examples: [4, 5, 7]),
(playoff:TEXT, Examples: [LCS, WCS, NHAF]),
(G:INTEGER, Examples: [12, 16, 18]),
(W:INTEGER, Examples: [4, 2, 3]),
(L:INTEGER, Examples: [8, 10, 1]),
(T:INTEGER, Examples: [0, 1, 2]),
(OTL:TEXT, Examples: [3, 4, 6]),
(Pts:INTEGER, Examples: [8, 4, 7]),
(SoW:TEXT, Examples: [3, 5, 2]),
(SoL:TEXT, Examples: [7, 5, 8]),
(GF:INTEGER, Examples: [79, 77, 59]),
(GA:INTEGER, Examples: [104, 83, 100]),
(name:TEXT, Examples: [Cobalt Silver Kings]),
(PIM:TEXT, Examples: [336, 27, 333]),
(BenchMinor:TEXT, Examples: [12, 14, 8]),
(PPG:TEXT, Examples: [28, 51, 42]),
(PPC:TEXT, Examples: [220, 279, 240]),
(SHA:TEXT, Examples: [4, 2, 5]),
(PKG:TEXT, Examples: [45, 43, 36]),
(PKC:TEXT, Examples: [242, 301, 267]),
(SHF:TEXT, Examples: [3, 8, 2])
]
# Table: TeamsHalf
[
(year:INTEGER, Primary Key, Examples: [1916, 1917, 1918]),
(lgID:TEXT, Examples: [NHA, NHL]),
(tmID:TEXT, Primary Key, Examples: [MOC, MOW, OT1]),
(half:INTEGER, Primary Key, Examples: [1, 2]),
(rank:INTEGER, Examples: [1, 3, 5]),
(G:INTEGER, Examples: [10, 4, 14]),
(W:INTEGER, Examples: [7, 3, 2]),
(L:INTEGER, Examples: [3, 7, 8]),
(T:INTEGER, Examples: [0]),
(GF:INTEGER, Examples: [58, 31, 56]),
(GA:INTEGER, Examples: [38, 42, 72])
]
# Table: Goalies
[
(playerID:TEXT, Primary Key, Examples: [abbotge01, abrahch01, adamsjo02]),
(year:INTEGER, Primary Key, Examples: [1943, 1974, 1975]),
(stint:INTEGER, Primary Key, Examples: [1, 2, 3]),
(tmID:TEXT, Examples: [BOS, NEW, WAS]),
(lgID:TEXT, Examples: [NHL, WHA, NHA]),
(GP:TEXT, Examples: [1, 16, 41]),
(Min:TEXT, Examples: [60, 870, 2385]),
(W:TEXT, Examples: [0, 8, 18]),
(L:TEXT, Examples: [1, 6, 18]),
(T/OL:TEXT, Examples: [0, 1, 2]),
(ENG:TEXT, Examples: [0, 1, 3]),
(SHO:TEXT, Examples: [0, 1, 2]),
(GA:TEXT, Examples: [7, 47, 136]),
(SA:TEXT, Examples: [504, 1221, 1438]),
(PostGP:TEXT, Examples: [1, 2, 11]),
(PostMin:TEXT, Examples: [1, 90, 34]),
(PostW:TEXT, Examples: [0, 6, 1]),
(PostL:TEXT, Examples: [0, 1, 5]),
(PostT:TEXT, Examples: [1, 0, 2]),
(PostENG:TEXT, Examples: [0, 1, 2]),
(PostSHO:TEXT, Examples: [0, 1, 2]),
(PostGA:TEXT, Examples: [0, 5, 1]),
(PostSA:TEXT, Examples: [51, 0, 14])
]
# Table: abbrev
[
(Type:TEXT, Primary Key, Examples: [Conference, Division, Playoffs]),
(Code:TEXT, Primary Key, Examples: [CC, EC, WA]),
(Fullname:TEXT, Examples: [Campbell Conference, Eastern Conference, Wales Conference])
]
# Table: Coaches
[
(coachID:TEXT, Primary Key, Examples: [abelsi01c, adamsja01c, agnewga01c]),
(year:INTEGER, Primary Key, Examples: [1952, 1953, 1957]),
(tmID:TEXT, Primary Key, Examples: [CHI, DET, STL]),
(lgID:TEXT, Examples: [NHL, WHA, NHA]),
(stint:INTEGER, Primary Key, Examples: [1, 2, 3]),
(notes:TEXT, Examples: [interim]),
(g:INTEGER, Examples: [70, 33, 74]),
(w:INTEGER, Examples: [27, 12, 16]),
(l:INTEGER, Examples: [28, 51, 12]),
(t:INTEGER, Examples: [15, 7, 5]),
(postg:TEXT, Examples: [7, 4, 6]),
(postw:TEXT, Examples: [3, 0, 2]),
(postl:TEXT, Examples: [4, 5, 6]),
(postt:TEXT, Examples: [0, 1, 2])
]
# Table: TeamVsTeam
[
(year:INTEGER, Primary Key, Examples: [1909, 1910, 1911]),
(lgID:TEXT, Examples: [NHA, PCHA, NHL]),
(tmID:TEXT, Primary Key, Examples: [COB, HAI, LES]),
(oppID:TEXT, Primary Key, Examples: [HAI, LES, MOS]),
(W:INTEGER, Examples: [1, 2, 0]),
(L:INTEGER, Examples: [1, 0, 2]),
(T:INTEGER, Examples: [0, 1, 2]),
(OTL:TEXT, Examples: [0, 1, 3])
]
# Table: ScoringSup
[
(playerID:TEXT, Examples: [actonke01, adamsgr01, allismi01]),
(year:INTEGER, Examples: [1988, 1989, 1987]),
(PPA:TEXT, Examples: [1, 5, 4]),
(SHA:TEXT, Examples: [1, 2, 4])
]
# Table: HOF
[
(year:INTEGER, Examples: [1969, 1960, 1959]),
(hofID:TEXT, Primary Key, Examples: [abelsi01h, adamsch01h, adamsja01h]),
(name:TEXT, Examples: [Sid Abel, Charles Adams, Jack Adams]),
(category:TEXT, Examples: [Player, Builder, Referee/Linesman])
]
# Table: AwardsPlayers
[
(playerID:TEXT, Primary Key, Examples: [abelsi01, alfreda01, amontto01]),
(award:TEXT, Primary Key, Examples: [First Team All-Star, Hart, Second Team All-Star]),
(year:INTEGER, Primary Key, Examples: [1948, 1949, 1941]),
(lgID:TEXT, Examples: [NHL, WHA]),
(note:TEXT, Examples: [tie, shared, Most Gentlemanly]),
(pos:TEXT, Examples: [C, LW, F])
]
【Foreign keys】
Scoring.year=Teams.year
Scoring.tmID=Teams.tmID
Scoring.playerID=Master.playerID
SeriesPost.year=Teams.year
SeriesPost.tmIDWinner=Teams.tmID
SeriesPost.year=Teams.year
SeriesPost.tmIDLoser=Teams.tmID
TeamsPost.year=Teams.year
TeamsPost.tmID=Teams.tmID
ScoringShootout.year=Teams.year
ScoringShootout.tmID=Teams.tmID
ScoringShootout.playerID=Master.playerID
AwardsCoaches.coachID=Coaches.coachID
Master.coachID=Coaches.coachID
ScoringSC.year=Teams.year
ScoringSC.tmID=Teams.tmID
ScoringSC.playerID=Master.playerID
TeamsSC.year=Teams.year
TeamsSC.tmID=Teams.tmID
TeamSplits.year=Teams.year
TeamSplits.tmID=Teams.tmID
GoaliesSC.year=Teams.year
GoaliesSC.tmID=Teams.tmID
GoaliesSC.playerID=Master.playerID
CombinedShutouts.IDgoalie1=Master.playerID
CombinedShutouts.IDgoalie2=Master.playerID
GoaliesShootout.year=Teams.year
GoaliesShootout.tmID=Teams.tmID
GoaliesShootout.playerID=Master.playerID
TeamsHalf.tmID=Teams.tmID
TeamsHalf.year=Teams.year
Goalies.year=Teams.year
Goalies.tmID=Teams.tmID
Goalies.playerID=Master.playerID
Coaches.year=Teams.year
Coaches.tmID=Teams.tmID
TeamVsTeam.year=Teams.year
TeamVsTeam.tmID=Teams.tmID
TeamVsTeam.oppID=Teams.tmID
TeamVsTeam.year=Teams.year
ScoringSup.playerID=Master.playerID
AwardsPlayers.playerID=Master.playerID

    【Question】
    What is the average BMI of all the coaches who have gotten in the Hall of Fame? average BMI = divide(sum(divide(weight, multiply(height, height))), count(coachID))

    【Evidence】
    average BMI = divide(sum(divide(weight, multiply(height, height))), count(coachID))

    Please read and understand the database schema carefully, and generate an executable SQL based on the user's question and evidence. 

SQL: SELECT SUM(T1.weight / (T1.height * T1.height)) / COUNT(T1.coachID) FROM Master AS T1 INNER JOIN HOF AS T2 ON T1.hofID = T2.hofID