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Long-term Debt - Additional Information (Details)
$ in Millions
9 Months Ended
Oct. 31, 2024
USD ($)
Sep. 30, 2024
USD ($)
Debt Instrument [Line Items]    
Description of borrowing capacity not subject to net leverage ratio covenant   In the event the Company’s outstanding indebtedness under the Revolver exceeds 35% of the aggregate principal amount of the revolving commitments then in effect, it is required to maintain a consolidated first lien leverage ratio no greater than 7.75 to 1.00.
Minimum [Member]    
Debt Instrument [Line Items]    
Debt instrument, net leverage ratio   0.01
Maximum [Member]    
Debt Instrument [Line Items]    
Debt instrument, net leverage ratio   0.0775
Revolver [Member]    
Debt Instrument [Line Items]    
Maturity Date   Jul. 31, 2026
Outstanding borrowing under revolver   $ 0.0
Maximum borrowing capacity under successor revolver   100.0
Amended Revolver [Member]    
Debt Instrument [Line Items]    
Maturity Date Oct. 31, 2029  
Description of borrowing capacity not subject to net leverage ratio covenant In the event the Company’s outstanding indebtedness under the Amended Revolver exceeds 40% of the aggregate principal amount of the revolving commitments then in effect, it is required to maintain a consolidated first lien leverage ratio no greater than 7.75 to 1.00.  
Maximum borrowing capacity under successor revolver $ 250.0  
Amended Revolver [Member] | Minimum [Member]    
Debt Instrument [Line Items]    
Debt instrument, net leverage ratio 0.01  
Amended Revolver [Member] | Maximum [Member]    
Debt Instrument [Line Items]    
Debt instrument, net leverage ratio 0.0775  
First Lien Credit Agreement [Member]    
Debt Instrument [Line Items]    
Maturity Date Oct. 31, 2031  
Term Loan $ 2,185.0  
First Lien Credit Agreement [Member] | Maximum [Member]    
Debt Instrument [Line Items]    
Interest rate 3.25%  
First Lien Credit Agreement [Member] | SOFR [Member] | Minimum [Member]    
Debt Instrument [Line Items]    
Interest rate 3.00%  
Term Loan due January 31, 2027 [Member]    
Debt Instrument [Line Items]    
Carrying amount of the amount outstanding under the facility   564.7
Term loan at time of issuance   $ 766.6
Maturity Date   Jan. 31, 2027
Term Loan due January 31, 2027 [Member] | LIBOR [Member] | Minimum [Member]    
Debt Instrument [Line Items]    
Interest rate   2.75%
Term Loan due January 31, 2027 [Member] | LIBOR [Member] | Maximum [Member]    
Debt Instrument [Line Items]    
Interest rate   3.00%