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Fair Value Measurements
9 Months Ended
Sep. 30, 2023
Fair Value Disclosures [Abstract]  
Fair Value Measurements Fair Value Measurements
The carrying values and estimated fair values of certain of our financial instruments were as follows (in millions):
September 30, 2023December 31, 2022
Carrying Value  Estimated Fair Value  Carrying ValueEstimated Fair Value  
Second Lien Notes (1)
$1,079.4 $1,102.7 $— $— 
First Lien Notes (1)
$— $— $542.4 $545.9 
Long-term debt$1,079.4 $1,102.7 $542.4 $545.9 
Long-term notes receivable from ARO (2)
$275.2 $429.9 $254.0 $336.7 

(1)The estimated fair value of the 8.375% Senior Secured Second Lien Notes due 2030 (the "Second Lien Notes") and Senior Secured First Lien Notes due 2028 (the "First Lien Notes"), which were redeemed in full on April 3, 2023, were determined using quoted market prices, which are level 1 inputs.

(2)The estimated fair value of our Notes Receivable from ARO was estimated using an income approach to value the forecasted cash flows attributed to the Notes Receivable from ARO using a discount rate based on a comparable yield with a country-specific risk premium, which are considered to be level 2 inputs.

The estimated fair values of our cash and cash equivalents, restricted cash, accounts receivable and trade payables approximated their carrying values as of September 30, 2023 and December 31, 2022.