Debt (Details)		1 Months Ended	3 Months Ended	4 Months Ended
	Dec. 31, 2023 USD ($)	Feb. 28, 2024	Mar. 31, 2024 USD ($)	Sep. 30, 2023	Mar. 31, 2024 KRW (₩)	Mar. 31, 2023	Mar. 31, 2022 USD ($)	Feb. 28, 2022 USD ($)	Apr. 30, 2021 KRW (₩) borrowing
Debt Instrument [Line Items]
Total debt	$ 1,209,785,000		$ 1,156,838,000
Less: Unamortized discount and deferred debt costs, net	(6,329,000)		(5,524,000)
Less: Short-term borrowings and current portion of long-term debt	(131,624,000)		(112,968,000)
Long-term debt	1,071,832,000		1,038,346,000
Collateralized debt			627,700,000
Asset Pledged as Collateral
Debt Instrument [Line Items]
Collateralized debt			319,000,000
Short-term term loans, variable rate | Japan | Subsidiary Term Loans
Debt Instrument [Line Items]
Total debt	5,098,000		4,136,000
Borrowing capacity available			$ 2,900,000
Short-term term loans, variable rate | Japan | Subsidiary Term Loans | Weighted Average
Debt Instrument [Line Items]
Weighted average interest rate (as a percent)			0.25%		0.25%
Short-term term loans, variable rate | Japan | TIBOR | Subsidiary Term Loans | Minimum
Debt Instrument [Line Items]
Interest rate spread (as a percent)			0.18%
Short-term term loans, variable rate | Japan | TIBOR | Subsidiary Term Loans | Maximum
Debt Instrument [Line Items]
Interest rate spread (as a percent)			0.20%
Senior Notes | 6.625% Senior notes, due September 2027
Debt Instrument [Line Items]
Interest rate (as a percent)			6.625%		6.625%
Total debt	525,000,000		$ 525,000,000
Subsidiary Term Loans | Term loan, fixed rate at 1.85%, due April 2024 | Korea
Debt Instrument [Line Items]
Interest rate (as a percent)			1.85%		1.85%
Total debt	0		$ 0
Face amount of debt | ₩									₩ 80,000,000,000
Number of annual borrowings | borrowing									6
Borrowing capacity available			$ 59,000,000		₩ 80,000,000,000
Subsidiary Term Loans | Term loan, fixed rate at 2.12%, due December 2028 | Korea
Debt Instrument [Line Items]
Interest rate (as a percent)			2.12%		2.12%
Total debt	200,000,000		$ 200,000,000
Subsidiary Term Loans | Term loan, fixed rate at 1.35%, due December 2024 | Japan
Debt Instrument [Line Items]
Interest rate (as a percent)			1.35%		1.35%
Total debt	40,414,000		$ 28,246,000
Subsidiary Term Loans | Term loan, fixed rate at 1.20%, due December 2025 | Japan
Debt Instrument [Line Items]
Interest rate (as a percent)			1.20%		1.20%
Total debt	30,913,000		$ 25,206,000
Subsidiary Term Loans | Term loan, fixed rate at 1.23%, due December 2026 | Japan
Debt Instrument [Line Items]
Interest rate (as a percent)			1.23%		1.23%
Total debt	55,729,000		$ 47,605,000
Subsidiary Term Loans | Term loan, fixed rate at 1.59%, due December 2027 | Japan
Debt Instrument [Line Items]
Interest rate (as a percent)			1.59%		1.59%
Total debt	89,053,000		$ 77,800,000
Subsidiary Term Loans | Term loan, fixed rate at 1.80%, due December 2028 | Japan
Debt Instrument [Line Items]
Interest rate (as a percent)			1.80%		1.80%
Total debt	124,078,000		$ 109,845,000
Subsidiary Term Loans | Term loans, SOFR plus 0.75%, weighted average of $6.06% as of March 31, 2024, due June 2025 | China
Debt Instrument [Line Items]
Total debt	37,000,000		$ 37,000,000
Subsidiary Term Loans | Term loans, SOFR plus 0.75%, weighted average of $6.06% as of March 31, 2024, due June 2025 | China | SOFR
Debt Instrument [Line Items]
Interest rate spread (as a percent)				0.75%
Weighted average interest rate (as a percent)			6.06%		6.06%
Subsidiary Term Loans | Term loans, SOFR plus 0.75%, weighted average of $6.06% as of March 31, 2024, due 2025 | China
Debt Instrument [Line Items]
Total debt	57,500,000		$ 57,000,000
Subsidiary Term Loans | Term loans, SOFR plus 0.75%, weighted average of $6.06% as of March 31, 2024, due 2025 | China | SOFR
Debt Instrument [Line Items]
Interest rate spread (as a percent)				0.75%
Weighted average interest rate (as a percent)			6.06%		6.06%
Subsidiary Term Loans | Term loans, SOFR plus 0.95% December 2026 | China
Debt Instrument [Line Items]
Total debt	$ 45,000,000		$ 45,000,000
Subsidiary Term Loans | Term loans, SOFR plus 0.95% December 2026 | China | Weighted Average
Debt Instrument [Line Items]
Weighted average interest rate (as a percent)			6.27%		6.27%
Subsidiary Term Loans | Term loans, SOFR plus 0.95% December 2026 | China | SOFR
Debt Instrument [Line Items]
Interest rate spread (as a percent)		0.95%
Subsidiary Term Loans | Term Loans, SOFR Plus 1.40%, Due December 2026 | China | SOFR
Debt Instrument [Line Items]
Interest rate spread (as a percent)	1.40%
Line of Credit | Credit facility, TAIFX plus the applicable bank rate, due December 2024 (Taiwan) | Revolving Credit Facility | Taiwan
Debt Instrument [Line Items]
Total debt	$ 0		$ 0
Borrowing capacity available			15,000,000
Credit facility, borrowing capacity							$ 15,000,000	$ 36,000,000
Line of Credit | $600.0 million senior secured revolving credit facility, applicable bank rate plus 1.75%, due March 2027 (Singapore) | Revolving Credit Facility | Singapore
Debt Instrument [Line Items]
Interest rate (as a percent)						1.75%
Total debt	$ 0		0
Borrowing capacity available			$ 600,000,000
Credit facility, borrowing capacity							600,000,000
Credit facility, base amount							$ 250,000,000
Credit facility percentage of variable borrowings							37.50%