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Pay vs Performance Disclosure - USD ($)
 12 Months Ended
Dec. 30, 2022
Dec. 31, 2021
Jan. 01, 2021
Pay vs Performance Disclosure [Table]      
Pay vs Performance [Table Text Block]
YearSummary Compensation Table Total for PEO ($) (1)Compensation Actually Paid to PEO ($) (2)Average Summary Compensation Table Total for Non-PEO NEOs ($) (3)Average Compensation Actually Paid to Non-PEO NEOs ($) (4)Value of Initial Fixed $100 Investment Based on:Net Income
(in millions)
($)		Annualized Recurring Revenue
(in millions)
($) (6)
Total Shareholder Return
($)		Peer Group Total Shareholder Return
($) (5)
202216,134,366(9,539,156)2,700,601(2,147,905)121139449.71,603.7
202113,956,82126,993,5473,551,9368,787,696209194492.71,409.1
202012,590,53725,198,1362,893,6079,291,939160144389.91,295.8
    
Named Executive Officers, Footnote [Text Block] The principal executive officer (“PEO”) of the Company for each year shown in the table was Robert G. Painter, the Company’s CEO.The non-PEO NEOs for each year shown in the table were:
202220212020
David G. BarnesDavid G. BarnesDavid G. Barnes
Ronald J. BisioSteven W. BerglundSteven W. Berglund
Jennifer LinManolis E. KotzabasakisJames Langley
Darryl R. MatthewsDarryl R. MatthewsDarryl R. Matthews
Manolis E. Kotzabasakis
James Langley
    
Peer Group Issuers, Footnote [Text Block] The peer group used for this data is the S&P 500 Information Technology Index, which is one of the peer groups used in the chart in Part II, Item 5 of the Company’s most recent Annual Report on Form 10-K.    
PEO Total Compensation Amount $ 16,134,366 $ 13,956,821 $ 12,590,537
PEO Actually Paid Compensation Amount $ (9,539,156) 26,993,547 25,198,136
Adjustment To PEO Compensation, Footnote [Text Block] Following are the adjustments made to the summary compensation table totals to determine the amounts shown as compensation actually paid for the PEO:
2022
($)		2021
($)		2020
($)
(A) Pension Plans—Present Value: Deduct the aggregate change in the actuarial present value of the accumulated benefit under all defined benefit and actuarial pension plansN/AN/AN/A
(B) Pension Plans—Service Costs: Add the aggregate of service cost and prior service cost for all defined benefit and actuarial pension plansN/AN/AN/A
(C) Equity Awards
(1) Deduct the amounts reported in the Summary Compensation Table under “Stock Awards” and “Option Awards”:-14,116,649-10,533,714-11,713,201
(i) Add the fair value as of the end of the year of all awards granted during the year that are outstanding and unvested as of the end of the year:+10,193,939+12,516,060+21,295,590
(ii) Add the amount equal to the change as of the end of the year (from the end of the prior year) in fair value of any awards granted in any prior year that are outstanding and unvested as of the end of the year:-20,592,123+8,340,367+1,994,385
(iii) Add, for awards that are granted and vest in the same year, the fair value as of the vesting date:———
(iv) Add the amount equal to the change as of the vesting date (from the end of the prior year) in fair value of any awards granted in any prior year for which all applicable vesting conditions were satisfied at the end of or during the year:-1,158,689+2,714,013+1,030,825
(v) Subtract, for any awards granted in any prior year that fail to meet the applicable vesting conditions during the year, the amount equal to the fair value at the end of the prior year:———
(vi) Add the dollar value of any dividends or other earnings paid on stock or option awards in the year prior to the vesting date that are not otherwise included in the total compensation for the year:———
Total adjustments:-25,673,522+13,036,726+12,607,599
    
Non-PEO NEO Average Total Compensation Amount $ 2,700,601 3,551,936 2,893,607
Non-PEO NEO Average Compensation Actually Paid Amount $ (2,147,905) 8,787,696 9,291,939
Adjustment to Non-PEO NEO Compensation Footnote [Text Block] Following are the adjustments made to the summary compensation table totals to determine the amounts shown as compensation actually paid to the non-PEO NEOs:
2022
($)		2021
($)		2020
($)
(A) Pension Plans—Present Value: Deduct the aggregate change in the actuarial present value of the accumulated benefit under all defined benefit and actuarial pension plansN/AN/AN/A
(B) Pension Plans—Service Costs: Add the aggregate of service cost and prior service cost for all defined benefit and actuarial pension plansN/AN/AN/A
(C) Equity Awards
(1) Deduct the amounts reported in the Summary Compensation Table under “Stock Awards” and “Option Awards”:-1,894,080-2,445,223-2,331,657
(i) Add the fair value as of the end of the year of all awards granted during the year that are outstanding and unvested as of the end of the year:+1,033,035+2,835,250+3,823,177
(ii) Add the amount equal to the change as of the end of the year (from the end of the prior year) in fair value of any awards granted in any prior year that are outstanding and unvested as of the end of the year:-2,104,280+1,233,812+3,590,670
(iii) Add, for awards that are granted and vest in the same year, the fair value as of the vesting date:———
(iv) Add the amount equal to the change as of the vesting date (from the end of the prior year) in fair value of any awards granted in any prior year for which all applicable vesting conditions were satisfied at the end of or during the year:-528,784+3,611,921+1,316,142
(v) Subtract, for any awards granted in any prior year that fail to meet the applicable vesting conditions during the year, the amount equal to the fair value at the end of the prior year:-1,354,397——
(vi) Add the dollar value of any dividends or other earnings paid on stock or option awards in the year prior to the vesting date that are not otherwise included in the total compensation for the year:———
Total adjustments:-4,848,506+5,235,760+6,398,332
    
Compensation Actually Paid vs. Total Shareholder Return [Text Block]
The following chart shows the relationship between the amounts calculated as compensation actually paid, for the PEO and for the non-PEO NEOs (averaged) and each of the Company’s total shareholder return and the peer group total shareholder return based on an initial $100 investment.
1649267451620
    
Compensation Actually Paid vs. Net Income [Text Block]
The following chart shows the relationship between the amounts calculated as compensation actually paid, for the PEO and for the non-PEO NEOs (averaged), and the Company’s net income.
4398046519701
    
Compensation Actually Paid vs. Company Selected Measure [Text Block]
The following chart shows the relationship between the amounts calculated as compensation actually paid, for the PEO and for the non-PEO NEOs (averaged), and the Company’s annualized recurring revenue (ARR).
4398046520522
    
Total Shareholder Return Vs Peer Group [Text Block]
The following chart shows the relationship between the amounts calculated as compensation actually paid, for the PEO and for the non-PEO NEOs (averaged) and each of the Company’s total shareholder return and the peer group total shareholder return based on an initial $100 investment.
1649267451620
    
Tabular List [Table Text Block]
MeasureExplanation
Annualized recurring revenue
See Appendix A for an explanation of annualized recurring revenue
RevenueThe Company’s revenue in a specified period
Operating incomeThe Company’s operating income in a specified period
Adjusted EBITDASee Appendix A for an explanation of Adjusted EBITDA
Total shareholder returnThe total shareholder return of the Company’s stock over a specified period
    
Total Shareholder Return Amount $ 121 209 160
Peer Group Total Shareholder Return Amount 139 194 144
Net Income (Loss) $ 449,700,000 $ 492,700,000 $ 389,900,000
Company Selected Measure Amount 1,603,700,000 1,409,100,000 1,295,800,000
PEO Name Robert G. Painter    
Additional 402(v) Disclosure [Text Block] See Appendix A to this proxy statement for an explanation of the company-selected measure “annualized recurring revenue.”    
Measure [Axis]: 1      
Pay vs Performance Disclosure [Table]      
Measure Name Annualized recurring revenue    
Measure [Axis]: 2      
Pay vs Performance Disclosure [Table]      
Measure Name Revenue    
Measure [Axis]: 3      
Pay vs Performance Disclosure [Table]      
Measure Name Operating income    
Measure [Axis]: 4      
Pay vs Performance Disclosure [Table]      
Measure Name Adjusted EBITDA    
Measure [Axis]: 5      
Pay vs Performance Disclosure [Table]      
Measure Name Total shareholder return    
PEO [Member]      
Pay vs Performance Disclosure [Table]      
Adjustment to Compensation Amount $ (25,673,522) $ 13,036,726 $ 12,607,599
PEO [Member] | Equity Awards Reported Value [Member]      
Pay vs Performance Disclosure [Table]      
Adjustment to Compensation Amount (14,116,649) (10,533,714) (11,713,201)
PEO [Member] | Equity Awards Granted During the Year, Unvested [Member]      
Pay vs Performance Disclosure [Table]      
Adjustment to Compensation Amount 10,193,939 12,516,060 21,295,590
PEO [Member] | Equity Awards Granted in Prior Years, Unvested [Member]      
Pay vs Performance Disclosure [Table]      
Adjustment to Compensation Amount (20,592,123) 8,340,367 1,994,385
PEO [Member] | Equity Awards Granted During the Year, Vested [Member]      
Pay vs Performance Disclosure [Table]      
Adjustment to Compensation Amount 0 0 0
PEO [Member] | Equity Awards Granted in Prior Years, Vested [Member]      
Pay vs Performance Disclosure [Table]      
Adjustment to Compensation Amount (1,158,689) 2,714,013 1,030,825
PEO [Member] | Equity Awards that Failed to Meet Vesting Conditions [Member]      
Pay vs Performance Disclosure [Table]      
Adjustment to Compensation Amount 0 0 0
PEO [Member] | Equity Awards, Value of Dividends and Other Earnings Paid Adjustment [Member]      
Pay vs Performance Disclosure [Table]      
Adjustment to Compensation Amount 0 0 0
Non-PEO NEO [Member]      
Pay vs Performance Disclosure [Table]      
Adjustment to Compensation Amount (4,848,506)    
Non-PEO NEO [Member] | Equity Awards Reported Value [Member]      
Pay vs Performance Disclosure [Table]      
Adjustment to Compensation Amount (1,894,080) (2,445,223) (2,331,657)
Non-PEO NEO [Member] | Equity Awards Granted During the Year, Unvested [Member]      
Pay vs Performance Disclosure [Table]      
Adjustment to Compensation Amount 1,033,035 2,835,250 3,823,177
Non-PEO NEO [Member] | Equity Awards Granted in Prior Years, Unvested [Member]      
Pay vs Performance Disclosure [Table]      
Adjustment to Compensation Amount (2,104,280) 1,233,812 3,590,670
Non-PEO NEO [Member] | Equity Awards Granted During the Year, Vested [Member]      
Pay vs Performance Disclosure [Table]      
Adjustment to Compensation Amount 0 0 0
Non-PEO NEO [Member] | Equity Awards Granted in Prior Years, Vested [Member]      
Pay vs Performance Disclosure [Table]      
Adjustment to Compensation Amount (528,784) 3,611,921 1,316,142
Non-PEO NEO [Member] | Equity Awards that Failed to Meet Vesting Conditions [Member]      
Pay vs Performance Disclosure [Table]      
Adjustment to Compensation Amount (1,354,397) 0 0
Non-PEO NEO [Member] | Equity Awards, Value of Dividends and Other Earnings Paid Adjustment [Member]      
Pay vs Performance Disclosure [Table]      
Adjustment to Compensation Amount $ 0 0 0
Non-PEO NEO [Member] | Equity Award Adjustments [Member]      
Pay vs Performance Disclosure [Table]      
Adjustment to Compensation Amount   $ 5,235,760 $ 6,398,332