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Business segments - Schedule of Segment Reporting Results By Segment (Details) $ in Thousands | 3 Months Ended | 12 Months Ended
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Sep. 30, 2019 USD ($) | Jun. 30, 2019 USD ($) | Mar. 31, 2019 USD ($) | Dec. 31, 2018 USD ($) | Sep. 30, 2018 USD ($) | Jun. 30, 2018 USD ($) | Mar. 31, 2018 USD ($) | Dec. 31, 2017 USD ($) | Sep. 30, 2019 USD ($) segment | Sep. 30, 2018 USD ($) | Sep. 30, 2017 USD ($)
Segment Reporting [Abstract] |  |  |  |  |  |  |  |  |  |  |
Number of business segments | segment |  |  |  |  |  |  |  |  | 3 |  |
Financial information for each of the Company's business segments |  |  |  |  |  |  |  |  |  |  |
Revenue | $ 754,966 | $ 730,710 | $ 736,520 | $ 664,619 | $ 558,446 | $ 597,855 | $ 612,787 | $ 623,148 | $ 2,886,815 | $ 2,392,236 | $ 2,450,961
Gross profit | 168,250 | 174,247 | 169,422 | 159,265 | 138,938 | 154,684 | 148,803 | 151,960 | 671,184 | 594,385 | 611,905
Selling, general and administrative expense |  |  |  |  |  |  |  |  | 321,023 | 285,241 | 284,593
Operating income | 77,576 | 83,594 | 81,801 | 74,136 | 61,908 | 82,571 | 71,321 | 79,683 | 317,107 | 295,483 | 313,512
Amortization of intangible assets |  |  |  |  |  |  |  |  | (33,054) | (10,308) | (12,208)
Gain on sale of a business |  |  |  |  |  |  |  |  | $ 0 | $ 0 | $ 650
Percentage of total revenue |  |  |  |  |  |  |  |  | 11.00% | 12.40% | 12.80%
Depreciation and amortization |  |  |  |  |  |  |  |  | $ 52,404 | $ 51,884 | $ 55,769
Other |  |  |  |  |  |  |  |  |  |  |
Financial information for each of the Company's business segments |  |  |  |  |  |  |  |  |  |  |
Selling, general and administrative expense | 475 | 503 | (394) | (599) | 865 | 1,032 | 0 | 0 | 2,676 | 2,844 | 1,492
Other |  |  |  |  |  |  |  |  | 15 | (1,897) | (1,409)
Segment Reconciling Items |  |  |  |  |  |  |  |  |  |  |
Financial information for each of the Company's business segments |  |  |  |  |  |  |  |  |  |  |
Amortization of intangible assets | (9,028) | (9,049) | (9,519) | (5,458) | (2,462) | (2,525) | (2,603) | (2,718) | (33,054) | (10,308) | (12,208)
Restructuring costs |  |  |  |  |  |  |  |  | 0 | (3,353) | (2,242)
Acquisition-related expenses | 0 | 0 | 0 | (2,691) | (947) | 0 | 0 | 0 | (2,691) | (947) | (83)
Gain on sale of a business |  |  |  |  |  |  |  |  | 0 | 0 | 650
U.S. Health and Human Services |  |  |  |  |  |  |  |  |  |  |
Financial information for each of the Company's business segments |  |  |  |  |  |  |  |  |  |  |
Revenue |  |  |  |  |  |  |  |  | 1,176,488 |  |
U.S. Health and Human Services | Operating segments |  |  |  |  |  |  |  |  |  |  |
Financial information for each of the Company's business segments |  |  |  |  |  |  |  |  |  |  |
Revenue | 300,406 | 291,132 | 290,737 | 294,213 | 288,944 | 314,477 | 306,249 | 304,241 | 1,176,488 | 1,213,911 | 1,220,086
Gross profit | 83,154 | 86,664 | 86,260 | 88,031 | 87,382 | 101,425 | 86,586 | 84,231 | 344,109 | 359,624 | 348,906
Selling, general and administrative expense |  |  |  |  |  |  |  |  | 123,275 | 140,990 | 144,014
Operating income | 53,832 | 54,250 | 56,860 | 55,892 | 52,195 | 67,043 | 49,970 | 49,426 | $ 220,834 | $ 218,634 | $ 204,892
Percentage of total revenue |  |  |  |  |  |  |  |  | 18.80% | 18.00% | 16.80%
Depreciation and amortization |  |  |  |  |  |  |  |  | $ 18,466 | $ 20,963 | $ 23,374
U.S. Federal Services |  |  |  |  |  |  |  |  |  |  |
Financial information for each of the Company's business segments |  |  |  |  |  |  |  |  |  |  |
Revenue |  |  |  |  |  |  |  |  | 1,111,197 |  |
U.S. Federal Services | Operating segments |  |  |  |  |  |  |  |  |  |  |
Financial information for each of the Company's business segments |  |  |  |  |  |  |  |  |  |  |
Revenue | 312,179 | 292,295 | 289,736 | 216,987 | 117,375 | 112,226 | 116,327 | 132,983 | 1,111,197 | 478,911 | 545,573
Gross profit | 66,586 | 66,803 | 60,696 | 47,985 | 33,690 | 32,276 | 27,374 | 33,358 | 242,070 | 126,698 | 139,321
Selling, general and administrative expense |  |  |  |  |  |  |  |  | 126,128 | 69,312 | 74,345
Operating income | 31,090 | 33,907 | 29,592 | 21,353 | 15,965 | 14,877 | 9,834 | 16,710 | $ 115,942 | $ 57,386 | $ 64,976
Percentage of total revenue |  |  |  |  |  |  |  |  | 10.40% | 12.00% | 11.90%
Depreciation and amortization |  |  |  |  |  |  |  |  | $ 16,802 | $ 8,478 | $ 11,175
Outside the U.S. |  |  |  |  |  |  |  |  |  |  |
Financial information for each of the Company's business segments |  |  |  |  |  |  |  |  |  |  |
Revenue |  |  |  |  |  |  |  |  | 599,130 |  |
Outside the U.S. | Operating segments |  |  |  |  |  |  |  |  |  |  |
Financial information for each of the Company's business segments |  |  |  |  |  |  |  |  |  |  |
Revenue | 142,381 | 147,283 | 156,047 | 153,419 | 152,127 | 171,152 | 190,211 | 185,924 | 599,130 | 699,414 | 685,302
Gross profit | 18,510 | 20,780 | 22,466 | 23,249 | 17,866 | 20,983 | 34,843 | 34,371 | 85,005 | 108,063 | 123,678
Selling, general and administrative expense |  |  |  |  |  |  |  |  | 68,944 | 72,095 | 64,742
Operating income | $ 2,157 | $ 4,989 | $ 4,474 | $ 4,441 | $ (945) | $ 4,208 | $ 16,440 | $ 16,265 | $ 16,061 | $ 35,968 | $ 58,936
Percentage of total revenue |  |  |  |  |  |  |  |  | 2.70% | 5.10% | 8.60%
Depreciation and amortization |  |  |  |  |  |  |  |  | $ 17,136 | $ 22,443 | $ 21,220

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