Summary of Significant Accounting Policies - Changes in accumulated other comprehensive income (loss) (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2022	Jan. 01, 2022	Jan. 02, 2021
Accumulated Other Comprehensive Income (Loss) [Line Items]
Accumulated other comprehensive loss	$ (278,472)	$ (359,084)	$ (488,428)
Other Comprehensive Income (Loss), before Reclassifications, Net of Tax	(66,954)	(96,839)
Gain/(loss) reclassified from accumulated other comprehensive income (effective portion)	13,658	32,505
Other Comprehensive Income (Loss), Net of Tax	80,612	129,344	(137,495)
Unrecognized pension benefit costs, Tax	1,995	39,470
Unrealized loss on interest rate swap, tax	16,836	(4,501)
Other Comprehensive Income (Loss), Defined Benefit Plan, Gain (Loss), Reclassification Adjustment from AOCI, Tax	37,500
Other Comprehensive Income (Loss), Cash Flow Hedge, Gain (Loss), Tax	21,337	8,619	(7,147)
Other Comprehensive Income (Loss), Unrealized Gain (loss) Certain Investments, Tax	(400)
Accumulated Foreign Currency Adjustment Attributable to Parent
Accumulated Other Comprehensive Income (Loss) [Line Items]
Accumulated other comprehensive loss	(205,345)	(97,654)	(49,961)
Other Comprehensive Income (Loss), before Reclassifications, Net of Tax	107,691	47,693
Gain/(loss) reclassified from accumulated other comprehensive income (effective portion)	0	0
Other Comprehensive Income (Loss), Net of Tax	(107,691)	(47,693)
Accumulated Defined Benefit Plans Adjustment Attributable to Parent
Accumulated Other Comprehensive Income (Loss) [Line Items]
Accumulated other comprehensive loss	(121,701)	(249,696)	(400,919)
Other Comprehensive Income (Loss), before Reclassifications, Net of Tax	117,840	137,187
Gain/(loss) reclassified from accumulated other comprehensive income (effective portion)	10,155	14,036
Other Comprehensive Income (Loss), Net of Tax	127,995	151,223
Accumulated Net Gain (Loss) from Cash Flow Hedges Attributable to Parent | Interest Rate Swap
Accumulated Other Comprehensive Income (Loss) [Line Items]
Accumulated other comprehensive loss	48,574	(13,064)	(37,548)
Other Comprehensive Income (Loss), before Reclassifications, Net of Tax	(58,135)	(6,015)
Gain/(loss) reclassified from accumulated other comprehensive income (effective portion)	3,503	18,469
Other Comprehensive Income (Loss), Net of Tax	61,638	24,484
AOCI, Accumulated Gain (Loss), Debt Securities, Available-for-sale, Parent
Accumulated Other Comprehensive Income (Loss) [Line Items]
Accumulated other comprehensive loss	0	1,330	$ 0
Other Comprehensive Income (Loss), before Reclassifications, Net of Tax	1,330	(1,330)
Gain/(loss) reclassified from accumulated other comprehensive income (effective portion)	0	0
Other Comprehensive Income (Loss), Net of Tax	$ (1,330)	$ 1,330