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

    【Schema】
    【DB_ID】 college_completion
【Schema】
# Table: institution_details
[
(unitid:INTEGER, Primary Key, Examples: [100654, 100663, 100690]),
(chronname:TEXT, Examples: [Alabama A&M University]),
(city:TEXT, Examples: [Normal, Birmingham, Montgomery]),
(state:TEXT, Examples: [Alabama, Alaska, Arizona]),
(level:TEXT, Examples: [4-year, 2-year]),
(control:TEXT, Examples: [Public]),
(basic:TEXT, Examples: [Masters Colleges and Universities--larger programs]),
(hbcu:TEXT, Examples: [X, NULL]),
(flagship:TEXT, Examples: [NULL, X]),
(long_x:REAL, Examples: [-86.568502, -86.80917, -86.17401]),
(lat_y:REAL, Examples: [34.783368, 33.50223, 32.362609]),
(site:TEXT, Examples: [www.aamu.edu/]),
(student_count:INTEGER, Examples: [4051, 11502, 322]),
(awards_per_value:REAL, Examples: [14.2, 20.9, 29.9]),
(awards_per_state_value:REAL, Examples: [18.8, 17.8, 15.9]),
(awards_per_natl_value:REAL, Examples: [21.5, 22.5, 16.5]),
(exp_award_value:INTEGER, Examples: [105331, 136546, 58414]),
(exp_award_state_value:INTEGER, Examples: [75743, 92268, 42194]),
(exp_award_natl_value:INTEGER, Examples: [66436, 101725, 37780]),
(exp_award_percentile:INTEGER, Examples: [90, 97, 30]),
(ft_pct:REAL, Examples: [93.8, 72.7, 62.7]),
(fte_value:INTEGER, Examples: [3906, 10032, 294]),
(fte_percentile:INTEGER, Examples: [33, 67, 12]),
(med_sat_value:TEXT, Examples: [823, 1146, NULL]),
(med_sat_percentile:TEXT, Examples: [0, 84, NULL]),
(aid_value:INTEGER, Examples: [7142, 6088, 2540]),
(aid_percentile:INTEGER, Examples: [72, 50, 1]),
(endow_value:TEXT, Examples: [NULL, 24136, 302]),
(endow_percentile:TEXT, Examples: [NULL, 93, 1]),
(grad_100_value:REAL, Examples: [10.0, 29.4, 0.0]),
(grad_100_percentile:INTEGER, Examples: [15, 67, 0]),
(grad_150_value:REAL, Examples: [29.1, 53.5, 66.7]),
(grad_150_percentile:INTEGER, Examples: [14, 66, 72]),
(pell_value:REAL, Examples: [71.2, 35.1, 68.4]),
(pell_percentile:INTEGER, Examples: [98, 39, 91]),
(retain_value:REAL, Examples: [63.1, 80.2, 37.5]),
(retain_percentile:INTEGER, Examples: [17, 70, 2]),
(ft_fac_value:REAL, Examples: [82.8, 92.4, 67.2]),
(ft_fac_percentile:INTEGER, Examples: [89, 98, 71]),
(vsa_year:TEXT, Examples: [2010, 2011, NULL]),
(vsa_grad_after4_first:TEXT, Examples: [14.7, 22.3, NULL]),
(vsa_grad_elsewhere_after4_first:TEXT, Examples: [2, 2.9, NULL]),
(vsa_enroll_after4_first:TEXT, Examples: [36.5, 34.2, NULL]),
(vsa_enroll_elsewhere_after4_first:TEXT, Examples: [16.1, 19.2, NULL]),
(vsa_grad_after6_first:TEXT, Examples: [33, 42.6, NULL]),
(vsa_grad_elsewhere_after6_first:TEXT, Examples: [5.3, 10.5, NULL]),
(vsa_enroll_after6_first:TEXT, Examples: [12.5, 7.9, NULL]),
(vsa_enroll_elsewhere_after6_first:TEXT, Examples: [14.6, 13.1, NULL]),
(vsa_grad_after4_transfer:TEXT, Examples: [15.7, NULL, 0]),
(vsa_grad_elsewhere_after4_transfer:TEXT, Examples: [1.5, NULL, 0]),
(vsa_enroll_after4_transfer:TEXT, Examples: [40.9, NULL, 0]),
(vsa_enroll_elsewhere_after4_transfer:TEXT, Examples: [17.2, NULL, 0]),
(vsa_grad_after6_transfer:TEXT, Examples: [36.4, NULL, 0]),
(vsa_grad_elsewhere_after6_transfer:TEXT, Examples: [5.6, NULL, 0]),
(vsa_enroll_after6_transfer:TEXT, Examples: [17.2, NULL, 0]),
(vsa_enroll_elsewhere_after6_transfer:TEXT, Examples: [11.1, NULL, 0]),
(similar:TEXT),
(state_sector_ct:INTEGER, Examples: [13, 16, 25]),
(carnegie_ct:INTEGER, Examples: [386, 106, 252]),
(counted_pct:TEXT, Examples: [99.7|07, 56.0|07, 100.0|07]),
(nicknames:TEXT, Examples: [NULL, UAB, UAH]),
(cohort_size:INTEGER, Examples: [882, 1376, 3])
]
# Table: state_sector_grads
[
(stateid:INTEGER, Examples: [1, 2, 4]),
(state:TEXT, Examples: [Alabama, Alaska, Arizona]),
(state_abbr:TEXT, Examples: [AL, AK, AZ]),
(control:TEXT, Examples: [Private for-profit]),
(level:TEXT, Examples: [4-year, 2-year]),
(year:INTEGER, Examples: [2011, 2012, 2013]),
(gender:TEXT, Examples: [B, F, M]),
(race:TEXT, Examples: [A, Ai, B]),
(cohort:TEXT, Examples: [4y bach, 4y other, 2y all]),
(grad_cohort:TEXT, Examples: [0, 1, 51]),
(grad_100:TEXT, Examples: [0, 2, 15]),
(grad_150:TEXT, Examples: [0, 3, 18]),
(grad_100_rate:TEXT, Examples: [NULL, 0, 3.9]),
(grad_150_rate:TEXT, Examples: [NULL, 0, 5.9]),
(grad_cohort_ct:INTEGER, Examples: [9, 16, 13])
]
# Table: institution_grads
[
(unitid:INTEGER, Examples: [100760, 101028, 101143]),
(year:INTEGER, Examples: [2011, 2012, 2013]),
(gender:TEXT, Examples: [B, M, F]),
(race:TEXT, Examples: [X, W, B]),
(cohort:TEXT, Examples: [2y all, 4y other, 4y bach]),
(grad_cohort:TEXT, Examples: [446, 185, 261]),
(grad_100:TEXT, Examples: [73, NULL, 40]),
(grad_150:TEXT, Examples: [105, 40, 65]),
(grad_100_rate:TEXT, Examples: [16.4, NULL, 6.7]),
(grad_150_rate:TEXT, Examples: [23.5, 21.6, 24.9])
]
# Table: state_sector_details
[
(stateid:INTEGER, Primary Key, Examples: [0, 1, 2]),
(state:TEXT, Examples: [United States, Alabama, Alaska]),
(state_post:TEXT, Examples: [U.S., Ala., Alaska]),
(level:TEXT, Primary Key, Examples: [2-year, 4-year]),
(control:TEXT, Primary Key, Examples: [Private for-profit]),
(schools_count:INTEGER, Examples: [632, 1180, 527]),
(counted_pct:TEXT, Examples: [NULL, 61, 62]),
(awards_per_state_value:TEXT, Examples: [NULL, 18.8, 17.8]),
(awards_per_natl_value:REAL, Examples: [21.5, 22.5, 24.6]),
(exp_award_state_value:TEXT, Examples: [NULL, 75743, 92268]),
(exp_award_natl_value:INTEGER, Examples: [66436, 101725, 38763]),
(state_appr_value:TEXT, Examples: [NULL, 290.68, 496.78]),
(state_appr_rank:TEXT, Examples: [NULL, 11, 2]),
(grad_rate_rank:TEXT, Examples: [23, 18, 8]),
(awards_per_rank:TEXT, Examples: [NULL, 42, 49])
]
【Foreign keys】
state_sector_grads.state=institution_details.state
state_sector_grads.stateid=state_sector_details.stateid
institution_grads.unitid=institution_details.unitid
state_sector_details.state=institution_details.state

    【Question】
    Give the name of the 4-year public school in "ID" with the lowest graduation 100 value. name of the school refers to chronname; 4-year refers to level = '4-year'; public refers to control = 'Public'; ID refers to state_abbr = 'ID'; lowest graduation 100 value refers to MIN(grad_100_value);

    【Evidence】
    name of the school refers to chronname; 4-year refers to level = '4-year'; public refers to control = 'Public'; ID refers to state_abbr = 'ID'; lowest graduation 100 value refers to MIN(grad_100_value);

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

SQL: SELECT T1.chronname FROM institution_details AS T1 INNER JOIN state_sector_grads AS T2 ON T2.state = T1.state WHERE T2.state_abbr = 'ID' AND T1.level = '4-year' AND T1.control = 'Public' GROUP BY T1.chronname ORDER BY SUM(T1.grad_100_value) ASC LIMIT 1