Shareholder Report, Holdings (Details)	Aug. 31, 2024
NETHERLANDS
Holdings [Line Items]
Percent of Net Asset Value	5.10%
AUSTRALIA
Holdings [Line Items]
Percent of Net Asset Value	4.90%
UNITED STATES
Holdings [Line Items]
Percent of Net Asset Value	4.60%
GREECE
Holdings [Line Items]
Percent of Net Asset Value	3.60%
SINGAPORE
Holdings [Line Items]
Percent of Net Asset Value	3.40%
FRANCE
Holdings [Line Items]
Percent of Net Asset Value	3.10%
NORWAY
Holdings [Line Items]
Percent of Net Asset Value	3.00%
Overseas SMA Completion Portfolio | ASR Nederland NV [Member]
Holdings [Line Items]
Percent of Net Asset Value	5.10%
Overseas SMA Completion Portfolio | Sankyo Co., Ltd. [Member]
Holdings [Line Items]
Percent of Net Asset Value	5.10%
Overseas SMA Completion Portfolio | Northern Star Resources Ltd. [Member]
Holdings [Line Items]
Percent of Net Asset Value	4.90%
Overseas SMA Completion Portfolio | TOPPAN Holdings, Inc. [Member]
Holdings [Line Items]
Percent of Net Asset Value	4.40%
Overseas SMA Completion Portfolio | DCC PLC [Member]
Holdings [Line Items]
Percent of Net Asset Value	4.20%
Overseas SMA Completion Portfolio | Dai-ichi Life Holdings, Inc. [Member]
Holdings [Line Items]
Percent of Net Asset Value	3.80%
Overseas SMA Completion Portfolio | TP Icap Group PLC [Member]
Holdings [Line Items]
Percent of Net Asset Value	3.80%
Overseas SMA Completion Portfolio | Shimamura Co., Ltd. [Member]
Holdings [Line Items]
Percent of Net Asset Value	3.70%
Overseas SMA Completion Portfolio | Piraeus Financial Holdings SA [Member]
Holdings [Line Items]
Percent of Net Asset Value	3.60%
Overseas SMA Completion Portfolio | Venture Corp., Ltd. [Member]
Holdings [Line Items]
Percent of Net Asset Value	3.40%
Overseas SMA Completion Portfolio | Financial Services Sector [Member]
Holdings [Line Items]
Percent of Net Asset Value	25.30%
Overseas SMA Completion Portfolio | Industrial Sector [Member]
Holdings [Line Items]
Percent of Net Asset Value	19.00%
Overseas SMA Completion Portfolio | Consumer Discretionary Sector [Member]
Holdings [Line Items]
Percent of Net Asset Value	12.60%
Overseas SMA Completion Portfolio | Information Technology Sector [Member]
Holdings [Line Items]
Percent of Net Asset Value	9.10%
Overseas SMA Completion Portfolio | Consumer Staples Sector [Member]
Holdings [Line Items]
Percent of Net Asset Value	8.30%
Overseas SMA Completion Portfolio | Materials Sector [Member]
Holdings [Line Items]
Percent of Net Asset Value	7.50%
Overseas SMA Completion Portfolio | Communications Sector [Member]
Holdings [Line Items]
Percent of Net Asset Value	4.50%
Overseas SMA Completion Portfolio | Healthcare Sector [Member]
Holdings [Line Items]
Percent of Net Asset Value	3.20%
Overseas SMA Completion Portfolio | Utilities Sector [Member]
Holdings [Line Items]
Percent of Net Asset Value	2.80%
Overseas SMA Completion Portfolio | Real Estate Sector [Member]
Holdings [Line Items]
Percent of Net Asset Value	2.30%
Overseas SMA Completion Portfolio | Unclassified Sector [Member]
Holdings [Line Items]
Percent of Net Asset Value	2.00%
Overseas SMA Completion Portfolio | Other [Member]
Holdings [Line Items]
Percent of Net Asset Value	8.60%
Overseas SMA Completion Portfolio | JAPAN
Holdings [Line Items]
Percent of Net Asset Value	40.10%
Overseas SMA Completion Portfolio | UNITED KINGDOM
Holdings [Line Items]
Percent of Net Asset Value	17.30%
Overseas SMA Completion Portfolio | GERMANY
Holdings [Line Items]
Percent of Net Asset Value	5.60%