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Shareholders' equity - Purchase of Equity Securities (Details) - EUR (€) € / shares in Units, € in Millions	1 Months Ended												2 Months Ended	3 Months Ended	4 Months Ended	5 Months Ended	6 Months Ended	7 Months Ended	8 Months Ended	9 Months Ended	10 Months Ended	11 Months Ended	12 Months Ended
	Dec. 31, 2024	Nov. 30, 2024	Oct. 31, 2024	Sep. 30, 2024	Aug. 31, 2024	Jul. 31, 2024	Jun. 30, 2024	May 31, 2024	Apr. 30, 2024	Mar. 31, 2024	Feb. 29, 2024	Jan. 31, 2024	Feb. 29, 2024	Mar. 31, 2024	Apr. 30, 2024	May 31, 2024	Jun. 30, 2024	Jul. 31, 2024	Aug. 31, 2024	Sep. 30, 2024	Oct. 31, 2024	Nov. 30, 2024	Dec. 31, 2024	Dec. 31, 2023
Equity [Abstract]
Total number of shares purchased (in shares)	0	0	0	0	0	0	0	0	106,109	196,519	217,359	54,938	272,297	468,816	574,925	574,925	574,925	574,925	574,925	574,925	574,925	574,925	574,925	1,620,128
Average price paid per share (Euro per share)	€ 0	€ 0	€ 0	€ 0	€ 0	€ 0	€ 0	€ 0	€ 905.71	€ 892.93	€ 849.36	€ 797.29											€ 869.68
Maximum value of shares that may yet be purchased (€ millions)	€ 10,300.0	€ 10,300.0	€ 10,300.0	€ 10,300.0	€ 10,300.0	€ 10,300.0	€ 10,300.0	€ 10,300.0	€ 10,300.0	€ 10,396.1	€ 10,571.6	€ 10,756.2

X

- Definition

Average price paid per share of shares purchased under the repurchase program.

+ References

No definition available.

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- Definition

Maximum Value Of Shares That May Yet Be Purchased Under Program

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- Definition

Number of shares that have been repurchased during the period and are being held in treasury.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-SubTopic 10
-Topic 505
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481112/505-10-50-2

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(29))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480566/210-10-S99-1

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 505
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.3-04)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480008/505-10-S99-1

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