Stock Compensation Plans and Stock Based Compensation (Details 1) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2022	Jan. 01, 2022	Jan. 02, 2021
Stock based compensation expense and allocation by cost
Stock-based compensation	$ 270,439	$ 210,090	$ 197,268
Cost of product and maintenance [Member]
Stock based compensation expense and allocation by cost
Stock-based compensation	3,818	3,375	2,922
Cost of services [Member]
Stock based compensation expense and allocation by cost
Stock-based compensation	4,851	4,161	3,720
Marketing and sales [Member]
Stock based compensation expense and allocation by cost
Stock-based compensation	54,771	43,264	42,096
Research and development [Member]
Stock based compensation expense and allocation by cost
Stock-based compensation	158,937	131,247	124,999
General and administrative [Member]
Stock based compensation expense and allocation by cost
Stock-based compensation	$ 48,062	$ 28,043	$ 23,531