Write SQL query to solve given problem: Give the name of the 4-year public school in "ID" with the lowest graduation 100 value.. Keep the solution inside sql tag ```sql [SQL-Query] ```
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