### Database Schema
CREATE TABLE institution_details
(
    unitid                               INTEGER
        constraint institution_details_pk
            primary key,
    chronname                            TEXT,
    city                                 TEXT,
    state                                TEXT,
    level                                TEXT,
    control                              TEXT,
    basic                                TEXT,
    hbcu                                 TEXT,
    flagship                             TEXT,
    long_x                               REAL,
    lat_y                                REAL,
    site                                 TEXT,
    student_count                        INTEGER,
    awards_per_value                     REAL,
    awards_per_state_value               REAL,
    awards_per_natl_value                REAL,
    exp_award_value                      INTEGER,
    exp_award_state_value                INTEGER,
    exp_award_natl_value                 INTEGER,
    exp_award_percentile                 INTEGER,
    ft_pct                               REAL,
    fte_value                            INTEGER,
    fte_percentile                       INTEGER,
    med_sat_value                        TEXT,
    med_sat_percentile                   TEXT,
    aid_value                            INTEGER,
    aid_percentile                       INTEGER,
    endow_value                          TEXT,
    endow_percentile                     TEXT,
    grad_100_value                       REAL,
    grad_100_percentile                  INTEGER,
    grad_150_value                       REAL,
    grad_150_percentile                  INTEGER,
    pell_value                           REAL,
    pell_percentile                      INTEGER,
    retain_value                         REAL,
    retain_percentile                    INTEGER,
    ft_fac_value                         REAL,
    ft_fac_percentile                    INTEGER,
    vsa_year                             TEXT,
    vsa_grad_after4_first                TEXT,
    vsa_grad_elsewhere_after4_first      TEXT,
    vsa_enroll_after4_first              TEXT,
    vsa_enroll_elsewhere_after4_first    TEXT,
    vsa_grad_after6_first                TEXT,
    vsa_grad_elsewhere_after6_first      TEXT,
    vsa_enroll_after6_first              TEXT,
    vsa_enroll_elsewhere_after6_first    TEXT,
    vsa_grad_after4_transfer             TEXT,
    vsa_grad_elsewhere_after4_transfer   TEXT,
    vsa_enroll_after4_transfer           TEXT,
    vsa_enroll_elsewhere_after4_transfer TEXT,
    vsa_grad_after6_transfer             TEXT,
    vsa_grad_elsewhere_after6_transfer   TEXT,
    vsa_enroll_after6_transfer           TEXT,
    vsa_enroll_elsewhere_after6_transfer TEXT,
    similar                              TEXT,
    state_sector_ct                      INTEGER,
    carnegie_ct                          INTEGER,
    counted_pct                          TEXT,
    nicknames                            TEXT,
    cohort_size                          INTEGER
)

CREATE TABLE institution_grads
(
    unitid        INTEGER,
    year          INTEGER,
    gender        TEXT,
    race          TEXT,
    cohort        TEXT,
    grad_cohort   TEXT,
    grad_100      TEXT,
    grad_150      TEXT,
    grad_100_rate TEXT,
    grad_150_rate TEXT,
    foreign key (unitid) references institution_details(unitid)
)

CREATE TABLE state_sector_grads
(
    stateid        INTEGER,
    state          TEXT,
    state_abbr     TEXT,
    control        TEXT,
    level          TEXT,
    year           INTEGER,
    gender         TEXT,
    race           TEXT,
    cohort         TEXT,
    grad_cohort    TEXT,
    grad_100       TEXT,
    grad_150       TEXT,
    grad_100_rate  TEXT,
    grad_150_rate  TEXT,
    grad_cohort_ct INTEGER,
    foreign key (state) references institution_details(state),
    foreign key (stateid) references state_sector_details(stateid)
)

CREATE TABLE "state_sector_details"
(
    stateid                INTEGER,
    state                  TEXT
        references institution_details (state),
    state_post             TEXT,
    level                  TEXT,
    control                TEXT,
    schools_count          INTEGER,
    counted_pct            TEXT,
    awards_per_state_value TEXT,
    awards_per_natl_value  REAL,
    exp_award_state_value  TEXT,
    exp_award_natl_value   INTEGER,
    state_appr_value       TEXT,
    state_appr_rank        TEXT,
    grad_rate_rank         TEXT,
    awards_per_rank        TEXT,
    primary key (stateid, level, control)
)

### Question
Among the institutes in the state of Alabama whose percent rank for median SAT value within sector is 77, how many of them have over 500 graduates in total in 2011?

### Hint
percent rank for median SAT value within sector refers to med_sat_percentile; over 500 graduates refers to grad_cohort > 500; in 2011 refers to year = 2011;

### SQL
SELECT COUNT(DISTINCT T1.chronname) FROM institution_details AS T1 INNER JOIN institution_grads AS T2 ON T2.unitid = T1.unitid WHERE T1.state = 'Alabama' AND T1.med_sat_percentile = '100' AND T2.year = 2011 AND T2.grad_cohort > 500