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);
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