How many years did Saul reign at the very most?

A significant event clearly established in time and clearly occurring prior to the anointing of Saul by Samuel: Eli dies and the Ark of the Covenant is taken by the Philistines: "And the Philistines fought... And the ark of God was taken; and the two sons of Eli, Hophni and Phinehas, were slain... Now Eli was ninety and eight years old... And it came to pass... that he fell from off the seat backward by the side of the gate, and his neck brake, and he died: for he was an old man, and heavy. And he had judged Israel forty years... And the ark of the Lord was in the country of the Philistines seven months... And the men of Kirjath-jearim came, and fetched up the ark of the Lord, and brought it into the house of Abinadab in the hill, and sanctified Eleazar his son to keep the ark of the Lord. And it came to pass, while the ark abode in Kirjath-jearim, that the time was long; for it was twenty years: and all the house of Israel lamented after the Lord..." 1 Sam. 4:10,11,15,18; 6:1; 7:2. "And David arose, and went with all the people that were with him from Baale of Judah [Baalah, which is Kirjath-Jearim... Kirjath-baal, which is Kirjath-jearim" Joshua 15:9,60 (KJV)], to bring up from thence the ark of God, whose name is called by the name of the Lord of host that dwelleth between the cherubims... And they brought it out of the house of Abinadab which was at Gibeah... And the ark of the Lord continued in the house of Obed-edom the Gittite three months: and the Lord blessed Obed-edom, and all his household... So David went and brought up the ark of God from the house of Obed-edom into the city of David with gladness... And David danced before the Lord... And as the ark of the Lord came into the city of David, Michal Saul's daughter looked through a window, and saw king David leaping and dancing before the Lord; and she despised him in her heart. And they brought in the ark of the Lord, and set it in his place, in the midst of the tabernacle that David had pitched for it:... Therefore Michal the daughter of Saul had no child unto the day of her death" 2 Sam 6:2,4,11,12,14,16,17,23 (KJV). NOTICE: From the above texts it can be seen that Eli died about 20 years and 10 months [7 month + 20 years + 3 months] before the ark was brought to the city of David.