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Schedule III Summary of Activity in Real Estate Facilities (Detail) - USD ($)
 1 Months Ended 9 Months Ended 12 Months Ended
Jan. 31, 2021
Sep. 30, 2023
Dec. 31, 2022
Dec. 31, 2021
Dec. 31, 2020
Real estate facilities          
Real estate facilities, Balance at beginning of year $ 1,210,102,582 $ 1,887,205,645 $ 1,593,623,628 $ 1,210,102,582 $ 1,173,825,368
Facility acquisitions 371,507,610   298,341,568 47,162,974 0
Impact of foreign exchange rate changes   (458,653) (12,984,154) (138,457) 4,147,798
Improvements and additions     8,224,603 12,151,893 32,129,416
Other facility acquisitions     69,981,850 [1] 15,689,143  
Disposition due to deconsolidation       (15,689,143)  
Real estate facilities, Balance at end of year   1,918,681,492 1,887,205,645 1,593,623,628 1,210,102,582
Accumulated depreciation          
Accumulated depreciation, beginning balance (115,903,045) (202,682,688) (155,926,875) (115,903,045) (83,692,491)
Depreciation expense   (39,331,373) (48,400,073) (40,158,233) (31,711,102)
Disposition due to deconsolidation       62,466  
Impact of foreign exchange rate changes   97,602 1,644,260 71,937 (499,452)
Accumulated depreciation, ending balance   (241,916,459) (202,682,688) (155,926,875) (115,903,045)
Construction in process          
Construction in process, Balance at beginning of year $ 1,761,303 4,490,926 1,799,004 1,761,303 12,237,722
Net additions and assets placed into service     2,691,922 37,701 (10,476,419)
Construction in process, Balance at end of year   6,085,298 4,490,926 1,799,004 1,761,303
Real estate facilities, net   $ 1,682,850,331 $ 1,689,013,883 $ 1,439,495,757 $ 1,095,960,840
[1] Such amount includes four individual property acquisitions completed during the year ended December 31, 2022.