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

    【Schema】
    【DB_ID】 california_schools
【Schema】
# Table: schools
[
(CDSCode:TEXT, Primary Key, Examples: [01100170000000, 01100170109835, 01100170112607]),
(NCESDist:TEXT, Examples: [0691051, 0600002, 0600003]),
(NCESSchool:TEXT, Examples: [10546, 10947, 12283]),
(StatusType:TEXT, Examples: [Active, Closed, Merged]),
(County:TEXT, Examples: [Alameda, Alpine, Amador]),
(District:TEXT),
(School:TEXT, Examples: [FAME Public Charter]),
(Street:TEXT, Examples: [313 West Winton Avenue]),
(StreetAbr:TEXT, Examples: [313 West Winton Ave.]),
(City:TEXT, Examples: [Hayward, Newark, Oakland]),
(Zip:TEXT, Examples: [94544-1136, 94560-5359, 94612-3355]),
(State:TEXT, Examples: [CA]),
(MailStreet:TEXT, Examples: [313 West Winton Avenue]),
(MailStrAbr:TEXT, Examples: [313 West Winton Ave.]),
(MailCity:TEXT, Examples: [Hayward, Newark, Oakland]),
(MailZip:TEXT, Examples: [94544-1136, 94560-5359, 94612]),
(MailState:TEXT, Examples: [CA]),
(Phone:TEXT, Examples: [(510) 887-0152, (510) 596-8901, (510) 686-4131]),
(Ext:TEXT, Examples: [130, 1240, 1200]),
(Website:TEXT, Examples: [www.acoe.org]),
(OpenDate:DATE, Examples: [2005-08-29]),
(ClosedDate:DATE, Examples: [2015-07-31]),
(Charter:INTEGER, Examples: [1, 0]),
(CharterNum:TEXT, Examples: [0728, 0811, 1049]),
(FundingType:TEXT, Examples: [Directly funded]),
(DOC:TEXT, Examples: [00, 31, 34]),
(DOCType:TEXT, Examples: [County Office of Education (COE)]),
(SOC:TEXT, Examples: [65, 66, 60]),
(SOCType:TEXT, Examples: [K-12 Schools (Public)]),
(EdOpsCode:TEXT, Examples: [TRAD, JUV, COMM]),
(EdOpsName:TEXT, Examples: [Traditional]),
(EILCode:TEXT, Examples: [ELEMHIGH, HS, ELEM]),
(EILName:TEXT, Examples: [Elementary-High Combination]),
(GSoffered:TEXT, Examples: [K-12, 9-12, K-8]),
(GSserved:TEXT, Examples: [K-12, 9-12, K-7]),
(Virtual:TEXT, Examples: [P, N, F]),
(Magnet:INTEGER, Examples: [0, 1]),
(Latitude:REAL, Examples: [37.658212, 37.521436, 37.80452]),
(Longitude:REAL, Examples: [-122.09713, -121.99391, -122.26815]),
(AdmFName1:TEXT, Examples: [L Karen, Laura, Clifford]),
(AdmLName1:TEXT, Examples: [Monroe, Robell, Thompson]),
(AdmEmail1:TEXT),
(AdmFName2:TEXT, Examples: [Sau-Lim (Lance), Jennifer, Annalisa]),
(AdmLName2:TEXT, Examples: [Tsang, Koelling, Moore]),
(AdmEmail2:TEXT),
(AdmFName3:TEXT, Examples: [Drew, Irma, Vickie]),
(AdmLName3:TEXT, Examples: [Sarratore, Munoz, Chang]),
(AdmEmail3:TEXT),
(LastUpdate:DATE, Examples: [2015-06-23])
]
# Table: frpm
[
(CDSCode:TEXT, Primary Key, Examples: [01100170109835, 01100170112607, 01100170118489]),
(Academic Year:TEXT, Examples: [2014-2015]),
(County Code:TEXT, Examples: [01, 02, 03]),
(District Code:INTEGER, Examples: [10017, 31609, 31617]),
(School Code:TEXT, Examples: [0109835, 0112607, 0118489]),
(County Name:TEXT, Examples: [Alameda, Alpine, Amador]),
(District Name:TEXT),
(School Name:TEXT, Examples: [FAME Public Charter]),
(District Type:TEXT, Examples: [County Office of Education (COE)]),
(School Type:TEXT, Examples: [K-12 Schools (Public)]),
(Educational Option Type:TEXT, Examples: [Traditional]),
(NSLP Provision Status:TEXT, Examples: [Breakfast Provision 2]),
(Charter School (Y/N):INTEGER, Examples: [1, 0]),
(Charter School Number:TEXT, Examples: [0728, 0811, 1049]),
(Charter Funding Type:TEXT, Examples: [Directly funded]),
(IRC:INTEGER, Examples: [1, 0]),
(Low Grade:TEXT, Examples: [K, 9, 1]),
(High Grade:TEXT, Examples: [12, 8, 5]),
(Enrollment (K-12):REAL, Examples: [1087.0, 395.0, 244.0]),
(Free Meal Count (K-12):REAL, Examples: [565.0, 186.0, 134.0]),
(Percent (%) Eligible Free (K-12):REAL, Examples: [0.519779208831647, 0.470886075949367, 0.549180327868853]),
(FRPM Count (K-12):REAL, Examples: [715.0, 186.0, 175.0]),
(Percent (%) Eligible FRPM (K-12):REAL, Examples: [0.657773689052438, 0.470886075949367, 0.717213114754098]),
(Enrollment (Ages 5-17):REAL, Examples: [1070.0, 376.0, 230.0]),
(Free Meal Count (Ages 5-17):REAL, Examples: [553.0, 182.0, 128.0]),
(Percent (%) Eligible Free (Ages 5-17):REAL, Examples: [0.516822429906542, 0.484042553191489, 0.556521739130435]),
(FRPM Count (Ages 5-17):REAL, Examples: [702.0, 182.0, 168.0]),
(Percent (%) Eligible FRPM (Ages 5-17):REAL, Examples: [0.65607476635514, 0.484042553191489, 0.730434782608696]),
(2013-14 CALPADS Fall 1 Certification Status:INTEGER, Examples: [1])
]
# Table: satscores
[
(cds:TEXT, Primary Key, Examples: [10101080000000, 10101080109991, 10101080111682]),
(rtype:TEXT, Examples: [D, S]),
(sname:TEXT, Examples: [FAME Public Charter]),
(dname:TEXT, Examples: [Alameda County Office of Education]),
(cname:TEXT, Examples: [Alameda, Amador, Butte]),
(enroll12:INTEGER, Examples: [398, 62, 75]),
(NumTstTakr:INTEGER, Examples: [88, 17, 71]),
(AvgScrRead:INTEGER, Examples: [418, 503, 397]),
(AvgScrMath:INTEGER, Examples: [418, 546, 387]),
(AvgScrWrite:INTEGER, Examples: [417, 505, 395]),
(NumGE1500:INTEGER, Examples: [14, 9, 5])
]
【Foreign keys】
frpm.CDSCode=schools.CDSCode
satscores.cds=schools.CDSCode

    【Question】
    How many schools with an average score in Math greater than 400 in the SAT test are exclusively virtual? Exclusively virtual refers to Virtual = 'F'

    【Evidence】
    Exclusively virtual refers to Virtual = 'F'

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

SQL: SELECT COUNT(DISTINCT T2.School) FROM satscores AS T1 INNER JOIN schools AS T2 ON T1.cds = T2.CDSCode WHERE T2.Virtual = 'F' AND T1.AvgScrMath > 400