SAMUEL AARON WILLIAMS
SELECTED WORKS
Smith Creek Pedestrian Bridge - w/ design/buildLAB at Virginia Tech - Clifton Forge, VA In a town physically divided by a deep creek, this design/build project provides a much needed infrastructural link within the urban fabric of Clifton Forge. The structure was conceived as an extension of the landscape, with impossibly thin planes rising from the earth to create a ramp, stair, and bridge. Randomly angled โtreeโ columns support the entire structure at a central hub, and reinforce the sense of transparency between structure and site. The design of the structural steel moment connections made the idea possible, and the entire structure was conceived, managed, and built by our student team.
ยฉJeff Goldberg/ESTO
ยฉJeff Goldberg/ESTO
ยฉJeff Goldberg/ESTO
Bailey Arts Park - Undergraduate Thesis (In Progress) - Winston-Salem, NC A study of contrasts, the project seeks to find a harmonious relationship between existing structures and new construction. On the site of an abandoned coal-fired power plant within Winston-Salemรข€™s densest urban district, a new tower provides residences and workspaces for visiting artists. Through this intervention a new social, programmatic, and geometric order is established, providing a framework for future development. The goal of the study is to build a deeper understanding of how construction, industry, and energy affect urban development and inform our understanding of place, time, and culture.
Bailey Arts Park - Undergraduate Thesis (In Progress) - Winston-Salem, NC - Continued
Amtrak Train Station - Charlottesville, VA
WELD B
B
B
EPDM Waterproofing Membrane
EPDM Waterproofing Membrane
Growing Medium, Planted 4"4" Growing Medium, Planted with Sedum Plants with Sedum Plants Drainage Mat with Filter Fabric Drainage Mat with Filter Fabric Ground Level Ground Level 0' - 0" 0' - 0"
Rigid Insulation 4"4" Rigid Insulation EPDM Waterproofing Membrane/ EPDM Waterproofing Membrane/ Root Barrier Root Barrier
TRAIN STATION FOR CHARLOTTESVILLE, VA
B
4"4" Concrete in 2" Deck Concrete in x2"6"x Composite 6" Composite Deck
HSS 6x6 Steel Column, HSS 6x6 Steel Column, 6" Metal Stud Infill Stud Infill 6" Metal
HSS6x6 Steel Column, 6" Metal StudStud Infill Infill HSS6x6 Steel Column, 6" Metal
Column Fully Welded to Welded Baseplate Column Fully to Baseplate
W12x22 Steel Girder W12x22 Steel Girder
1" x 12" x12" Baseplate 1" xSteel 12" x12" Steel Baseplate
W8x24 Steel Beam, Painted White
W8x24 Steel Beam, Painted White 1" Non-Shrink Grout
Bolted Gusset Plate Connection
1" Non-Shrink Grout
Bolted Gusset Plate Connection
Wet-Set Anchor Bolts
Wet-Set Anchor Bolts
Roof Level 2 Roof 15'Level - 0" 2
15' - 0"
18" x 18" Cast-In-Place Concrete 18" x 18" Cast-In-Place Concrete Column Below
AMTRAK
Column Below
1
1
Detail Section - Wall Opening
1 1/2"Section = 1'-0" - Wall Opening Detail 1 1/2" = 1'-0"
2
Detail Section - Wall to Floor Deck 1 1/2" = 1'-0" Detail Section - Wall to Floor Deck
2
1 1/2" = 1'-0"
ARCHITECTURE GROUP
This transportation hub was inspired by the image of a train barreling through the mountains of the Appalachian region in which the station resides. The idea is realized as a massive wall running through the long narrow site. This wall contains all the necessary service elements of the building, and creates a divide between spaces belonging to the train and spaces belonging to the town. The resulting primary environments are by contrast extremely light, fully glazed, and geometrically pure, opening outward to the train and the surrounding urban area.
Shenandoah Autism Center - Clifton Forge, VA This school for students with autism was proposed as part of a feasibility study for a current school looking to expand. Faced with the challenge of few available building sites, the project addresses the problem of a steep, mountainside site by organizing all program elements into a long bar running perpendicular to the slope of the topography. By slightly separating walls, storage elements, and the roof, the schoolรข€™s need for individualized classrooms is satisfied while maintaining a sense of spatial openness and connectivity throughout the entire school.
Rapunzel Writerโs Retreat - Eggleston, VA A series of these single-person dwellings were developed as part of a master plan for a writerโs retreat in the small, former resort town of Eggleston, VA. This house and studio seeks to create an atmosphere of extreme introversion by placing each program element on its own individual floor deck. The floor platforms are then suspended in succession from the roof structure, and are entirely independent of the exterior shell and circulation of the house. This โworld within a worldโ creates a strong sense of inward focus and a place of serene isolation for the artist.
Visitorรข€™s Center - Warm Springs Mountain Preserve - Bath County, VA This competition entry seeks harmony with its unique site - a barren and secluded plateau at the peak of a mountain wildlife preserve. The buildingรข€™s asymmetrical gabled form echoes the form of the mountain ridge on which it rests. Copper cladding on all exterior surfaces allows it to visually weather and tarnish over time, becoming an inseparable part of the nature of the mountain. A rough, board-formed concrete wall surrounds the site, separating it visually and sonically from the neighboring airfield, heightening the sense of seclusion and protection, and providing opportunities to frame spectacular views to the north.
Redirection of Motor Row - w/ CHICAGO STUDIO - Chicago, IL The once-glamorous Motor Row district of Chicago now occupies a prime stretch of Michigan Avenue as a series of derelict, empty building shells with magnificent historic facades. Tasked with creating a strategy for redirecting this building stock towards sustainable development, an รข€œinside-outรข€? approach was devised in which particularly rich and specific architectural conditions are given precedence over the master plan. This strategy allowed for the unpredictable insertion of new programmatic elements into the existing shells, and creates a series of layered thresholds that heighten the sense of history and culture in the area.
68
RESIDENTIAL
HT
OF
GA
CO
concept diagram - layering of thresholds
LIG RO
UR
T
RD
EN
E
WIN B
U
BL
programmatic diagram
ICH
T
AN
UR
TA
ES
-R
AN
IG
LU
C ES
R BA
UE
EN
AV
M
daylighting - selective subtraction of mass
70
71
concept diagram - served and service space 69
Hotel Proposal - w/ GREC Architects - Chicago, IL Created as a response to a request for proposals by a major Chicago developer, these studies for a hotel within a fast-growing area of the city serve as a proof of concept for our teamรข€™s design proposal. The key goals driving these preliminary sketches were to maximize the room count within the given zoning regulations, to respond appropriately to the surrounding context and building styles, and to provide infrastructural links and amenities to serve future growth in the area.
๏๏๏๏๏๏๏ ๏๏๏๏๏๏๏๏๏๏๏๏๏ฅ๏๏
๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏ ๏๏๏๏๏๏๏ ๏๏๏ ๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏ก๏๏๏๏๏๏ข๏ฃ ๏๏ข๏ ๏๏๏ข๏๏๏๏๏ ๏๏๏๏๏๏๏
๏๏๏๏๏๏๏๏๏๏๏ ๏๏๏๏๏๏๏ ๏๏๏ ๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏ก๏๏๏๏๏๏ข๏ฃ ๏๏ข๏ ๏๏๏ข๏๏๏๏๏ ๏๏๏๏๏๏๏
๏๏๏๏๏ค๏๏๏
๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏ ๏๏๏๏๏๏๏๏๏๏๏ข๏๏๏๏
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๏๏๏ค๏๏๏๏ ๏๏
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๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏ข ๏๏๏๏๏๏๏๏๏๏๏ข๏๏๏๏๏๏
๏๏
McCreary Field House at Wake Forest - w/ Walter Robbs Architects - Winston-Salem, NC ๏๏๏๏๏
๏๏๏๏
๏ ๏๏๏๏๏๏๏๏๏๏ข๏๏ฅ๏๏๏๏ ๏ ๏๏๏๏๏๏๏
๏๏๏๏๏
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๏๏๏๏๏๏๏๏ ๏๏๏๏๏๏๏ ๏ฅ๏ ๏๏๏๏๏๏๏๏๏๏๏ ๏๏๏๏๏ ๏๏๏๏๏ ๏๏๏ง
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๏๏๏๏๏๏๏๏๏๏๏๏๏ข ๏๏๏๏๏๏๏๏๏๏ ๏๏๏
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๏๏๏๏๏๏
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๏๏๏๏๏๏๏๏๏๏๏๏๏
๏ ๏๏ก๏ ๏ข๏ ๏๏ฃ๏๏๏ก๏
๏ ๏๏๏ค๏๏ ๏๏๏๏
๏๏๏๏ ๏๏๏๏๏๏๏๏๏๏๏๏๏ข๏๏๏๏ ๏๏๏๏ข๏๏ฆ๏๏๏ ๏๏๏๏๏๏๏๏๏๏๏๏ค๏๏
๏ข๏๏๏
๏๏๏๏ ๏๏๏๏
๏ค๏๏๏๏๏๏๏๏๏๏๏๏๏๏
My time spent working on this indoor practice football facility for Wake Forest University consisted of the production of design development and construction document sets within a BIM environment. My responsibilities on the project included the documentation and detailing of all associated site work, interior and exterior elevations and associated details, window and frame types, modeling of existing building elements, management of linked architectural and consultantโs models, and sheet management. ๏๏๏๏๏๏๏๏๏๏๏๏๏ ๏ ๏๏๏๏๏๏๏ ๏๏๏ ๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏ ๏ก๏๏๏๏๏๏ข๏ฃ๏๏๏ข๏ ๏ ๏ข๏๏๏๏๏ ๏๏๏๏๏๏๏
๏๏๏๏๏
๏๏๏๏๏๏๏๏๏๏๏
๏๏๏๏๏๏๏๏ ๏๏๏๏๏๏๏ ๏ฅ๏ ๏๏๏ง๏๏๏๏๏ ๏๏๏๏๏๏๏๏๏ฆ๏ ๏๏๏๏๏ ๏๏๏๏๏๏๏๏๏๏
๏๏๏๏๏๏๏
๏๏
๏๏๏๏๏
๏๏๏๏๏๏๏๏ ๏๏๏๏๏๏๏ ๏ฅ๏ ๏๏๏๏๏๏๏๏๏๏๏ ๏ง๏๏๏๏๏๏๏๏ ๏๏๏ง
๏๏๏๏ฌ๏๏ ๏๏๏๏๏๏๏๏๏๏ข๏๏ ๏๏๏๏๏๏๏๏๏๏๏๏๏๏
๏๏๏๏๏
๏๏๏๏๏
๏๏๏๏ ๏๏๏ค๏๏๏๏ ๏๏๏
๏๏๏๏๏๏๏ ๏๏๏๏๏๏ ๏ฌ๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏
๏๏๏๏๏
๏๏
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๏๏๏ค๏๏๏๏ ๏๏
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๏๏๏๏๏๏๏ซ๏๏๏๏๏๏๏๏๏จ๏๏๏๏๏๏๏๏๏๏๏๏๏
๏ ๏๏ ๏๏ ๏๏ก๏ ๏ข๏ ๏๏ฃ๏๏๏ก๏
๏๏
๏๏
๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏ข ๏๏๏๏๏๏๏๏๏๏๏ข๏๏๏๏๏๏
๏ ๏๏ก๏ ๏ข๏ ๏๏ฃ๏๏๏ก๏
๏๏๏๏๏
๏๏๏๏๏
๏๏๏๏๏
๏๏๏๏๏ค๏๏๏ ๏๏๏๏๏๏๏๏๏๏๏ข๏๏๏๏
๏๏๏๏๏๏๏ ๏๏๏๏๏๏๏๏ ๏ฅ๏ ๏๏๏ง๏๏๏๏๏ ๏๏๏๏๏ ๏๏๏๏๏ ๏๏๏๏๏๏๏๏๏๏
๏๏จ
๏๏๏๏๏๏๏๏๏๏๏๏๏
๏๏๏๏๏๏๏๏ซ๏๏๏๏๏๏๏๏๏๏๏๏ข๏๏ ๏๏๏๏๏๏ข๏๏๏๏๏๏๏๏๏
๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏ ๏๏๏๏๏๏๏ ๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏ ๏ก๏๏๏๏๏๏ข๏ฃ๏๏๏ข๏ ๏ ๏ข๏๏๏๏๏ ๏๏๏๏๏๏๏
๏ ๏๏ ๏๏ ๏๏ก๏ ๏ข๏ ๏๏ฃ๏๏๏ก๏
๏๏๏๏ ๏๏๏๏๏ ๏๏๏๏ญ๏๏๏๏๏
๏๏๏๏๏๏๏๏ฆ ๏ฆ๏๏๏ฃ๏๏๏๏๏๏ค๏ฃ๏๏๏๏ ๏๏๏๏ก๏๏๏๏ก๏๏ฅ๏๏๏๏๏๏๏
๏๏๏๏๏
๏๏๏๏๏๏๏๏
๏๏๏๏๏๏๏๏๏๏๏๏๏
๏๏๏๏๏๏
๏๏๏๏๏
๏๏๏๏๏ ๏๏๏๏๏
๏ ๏
๏
๏
๏ฉ๏๏ค
๏
๏๏๏๏๏๏๏๏ ๏๏๏๏๏๏๏ ๏ฅ๏ ๏๏๏๏๏๏ ๏๏๏๏๏๏๏๏๏ฆ๏ ๏๏๏๏๏ ๏ง๏๏๏๏๏๏๏
๏
๏ ๏๏ ๏๏ ๏๏ก๏ ๏ข๏ ๏๏ฃ๏๏๏ก๏
๏
๏
๏
๏
๏๏๏๏๏๏ ๏ช๏๏
๏๏
๏ ๏๏๏๏๏๏๏ช๏๏
๏ค๏๏๏๏๏๏ฃ๏๏๏๏ค๏๏
๏ ๏
๏๏๏
๏๏ ๏๏
๏
๏ฅ๏๏ข๏ค๏๏๏๏๏๏๏๏ ๏๏ซ๏๏๏๏ข๏๏๏๏ฃ๏๏๏๏ก๏๏๏๏ข๏
๏๏๏๏๏
๏๏๏๏๏ ๏๏๏๏๏๏๏๏ค๏๏๏ค๏๏๏๏ ๏จ๏๏๏๏ค๏๏๏๏ข๏ค๏๏๏๏๏๏ ๏ ๏๏๏๏๏
๏๏๏
๏ค๏
๏ค๏
๏ค๏ ๏ ๏ฉ ๏๏๏๏
๏๏
๏๏๏๏
๏
๏
๏
๏
๏ ๏
๏๏
๏๏๏๏
๏๏๏๏
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๏๏๏๏๏๏๏ ๏๏๏๏ ๏๏๏ฅ๏๏ฆ๏๏๏ข
๏
๏
๏ก
๏ค๏
๏ค
๏ค๏ ๏ค๏ ๏ค๏ ๏ค๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏ฅ๏๏ ๏๏๏๏๏๏๏ข๏๏๏๏๏๏๏๏ก๏๏๏๏๏๏๏๏๏๏๏๏ ๏ฅ๏๏ข๏ค๏๏๏๏๏๏๏๏
๏ก๏๏๏๏๏๏ข๏ฃ๏๏๏ข๏ ๏ ๏ข๏๏๏๏๏ ๏๏๏๏๏๏๏ ๏ค๏๏๏๏๏๏๏๏๏๏๏๏๏๏
๏ฅ๏๏๏๏ฏ๏๏ค๏๏๏๏๏
๏ ๏
๏ค๏
๏๏ฃ๏๏๏ฃ๏๏๏ค๏ฃ๏๏ค๏๏๏๏ ๏๏๏ก๏๏ค๏ฅ๏๏๏๏ค๏๏๏๏๏ก๏ ๏๏๏๏๏๏
๏
๏๏๏๏๏๏๏ ๏๏
๏๏จ
๏๏๏๏
๏ ๏๏ ๏๏ ๏๏ก๏ ๏ข๏ ๏
๏๏ ๏๏๏ ๏
๏๏๏๏๏๏๏๏๏๏ฅ
๏๏๏๏๏๏๏๏๏
๏๏๏๏๏๏๏๏๏
๏๏๏๏
๏๏๏๏๏๏๏๏๏๏ ๏๏๏๏๏๏๏๏๏๏๏ ๏ก๏๏๏๏๏๏ข๏ฃ๏๏ ๏ ๏๏๏๏๏๏๏
๏ค๏๏๏๏๏๏๏๏๏๏
๏๏๏๏
๏
๏๏๏๏๏๏๏ ๏๏
๏ค๏
๏๏๏๏
๏ ๏
๏๏๏๏
๏
๏๏๏๏๏๏๏ ๏๏๏๏๏๏
๏๏๏๏๏๏๏๏ค๏๏๏ค๏๏๏๏ ๏จ๏๏๏๏ค๏๏๏๏ข๏ค๏๏๏๏๏๏ ๏ ๏๏๏๏๏
๏๏๏๏ฌ๏๏ ๏๏๏๏๏๏๏๏๏๏ข๏๏ ๏๏๏๏๏๏๏๏๏๏๏๏๏๏ ๏๏๏๏๏ ๏๏๏๏๏ง๏๏๏๏๏๏๏จ๏๏๏๏ ๏๏๏๏๏ ๏๏๏๏๏๏๏๏๏ฉ๏๏๏ช๏๏๏๏๏๏ ๏๏๏ซ๏๏ค๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏
๏๏๏๏๏๏๏๏๏๏๏๏๏ ๏๏ ๏๏๏ก๏๏ข๏ฃ๏๏ค๏๏๏ฅ๏๏๏ฃ๏
๏
๏๏๏๏๏๏๏๏๏
๏๏๏๏๏๏๏๏๏๏๏ ๏๏๏๏๏๏
๏๏๏๏๏
๏๏จ๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏
๏๏๏๏๏๏
๏๏
๏ค๏ ๏ค๏ ๏๏๏๏๏๏๏๏๏๏๏๏๏
๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏ ๏๏๏๏๏๏๏ ๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏ ๏๏ ๏๏๏๏
๏๏
๏๏๏
๏๏๏๏๏
๏๏
๏๏๏๏
๏
๏๏๏๏๏
๏ก
๏๏๏๏ช๏
๏๏๏๏
๏๏๏
๏๏๏๏๏ก๏ข๏๏ฃ๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏
๏
๏๏๏๏๏
๏๏๏๏๏๏ซ๏๏๏๏๏๏๏๏๏๏ข๏๏๏๏๏๏๏๏๏ข ๏๏๏๏๏๏๏๏
๏๏ฉ
๏๏๏๏๏
๏
๏๏๏๏๏ค๏๏๏
๏๏๏๏๏๏๏ ๏๏๏๏ ๏๏๏ฅ๏๏ฆ๏๏๏ข
๏ ๏ฉ
๏๏๏
๏
๏ค๏ฃ๏๏ค๏๏๏๏๏๏๏๏๏๏ ๏๏๏๏ฅ๏๏ค๏ ๏๏ ๏๏ ๏๏๏ฃ๏๏๏๏๏
๏๏๏๏๏๏๏๏๏๏๏๏๏ ๏๏
๏๏๏๏ฌ๏๏ ๏๏๏ ๏๏๏๏๏๏๏๏๏
๏ฃ
๏๏๏๏๏๏๏๏๏๏๏ข๏๏๏๏ ๏ค๏
๏๏๏๏๏๏๏๏ซ๏๏๏๏๏๏๏๏๏๏๏๏ข๏๏ ๏๏๏๏๏๏ข๏๏๏๏๏๏๏๏๏
๏๏๏ก๏๏ข๏ฃ๏๏ค๏๏๏ฅ๏๏๏ฃ๏
๏๏๏๏ ๏๏๏ค๏๏
๏ ๏๏๏๏๏
๏ค
๏ค๏ฃ๏ก๏๏๏ค๏๏๏๏๏๏๏๏
๏๏
๏๏๏ ๏๏๏ ๏๏๏๏๏๏ ๏๏๏๏๏๏ ๏ ๏๏๏๏๏ ๏
๏๏๏๏๏๏๏๏๏๏ ๏๏๏๏๏๏
๏ฃ
๏๏๏๏๏๏๏ ๏๏
๏ฅ๏๏ข๏ค๏๏๏๏๏๏๏๏ ๏ข๏๏๏๏๏๏๏๏ค๏๏๏๏๏๏๏๏๏๏
๏๏๏๏๏๏๏ซ๏๏๏ ๏๏๏๏๏๏
๏ ๏
๏๏๏ ๏๏๏
๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏ ๏๏๏๏๏๏๏ ๏๏๏๏๏๏
๏ ๏
๏๏๏๏๏
๏ค๏๏๏๏๏๏๏๏๏ ๏๏๏๏๏๏๏๏ ๏๏๏๏๏๏๏ ๏ฅ๏ ๏๏๏๏๏๏๏๏๏๏๏ ๏ง๏๏๏๏๏๏๏๏ ๏๏๏ง ๏ ๏๏ก๏ ๏ข๏ ๏๏ฃ๏๏๏ก๏
A
๏๏๏๏๏๏๏๏ ๏๏๏๏๏๏๏ ๏ฅ๏ ๏๏๏ง๏๏๏๏๏ ๏๏๏๏๏๏๏๏๏ฆ๏ ๏๏๏๏๏ ๏๏๏๏๏๏๏๏๏๏ ๏๏๏๏๏๏๏๏ ๏๏๏๏๏๏๏ ๏ฅ๏ ๏๏๏๏๏๏ ๏๏๏๏๏๏๏๏๏ฆ๏ ๏๏๏๏๏ ๏๏๏๏ ๏๏๏ฉ ๏ ๏ ๏๏ฉ ๏ ๏ ๏ ๏ ๏ ๏ ๏ ๏ ๏๏ค ๏
๏ ๏๏ ๏๏ ๏๏ก๏ ๏ข๏ ๏๏ฃ๏๏๏ก๏ ๏ ๏๏ ๏๏ ๏๏ก๏ ๏ข๏ ๏๏ฃ๏๏๏ก๏
๏๏
๏๏๏๏๏๏๏ ๏๏๏
๏๏๏๏๏๏๏๏๏๏๏๏ค๏๏๏๏ ๏๏๏๏๏๏๏ค๏๏๏ฅ๏๏ข๏ค๏
๏ง๏๏๏ค๏๏๏ข๏๏๏๏๏๏๏๏๏๏ ๏ค๏ฃ๏๏๏๏๏๏ช๏ฃ๏๏๏๏๏ ๏๏๏๏๏๏๏๏๏ค๏๏๏๏๏
๏๏๏
๏ฉ
๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏ข ๏๏๏๏๏๏๏๏๏๏๏ข๏๏๏๏๏๏
๏
๏๏ง๏๏ข๏ค๏๏๏๏๏๏ ๏๏๏๏๏๏๏ค๏๏๏๏๏๏๏๏ ๏๏ง๏๏๏๏๏๏๏๏ข๏๏
๏ ๏ฉ
๏
๏
๏๏๏๏๏ง๏๏๏๏ ๏๏๏๏๏ ๏๏๏๏ ๏๏๏ซ๏๏ค๏๏๏๏๏
๏ ๏๏๏๏๏๏๏๏๏๏ ๏๏๏๏๏๏
๏๏๏๏๏
๏๏๏๏ฌ๏๏ ๏๏๏๏ ๏๏๏๏๏๏๏๏๏๏
๏๏๏๏๏๏
๏
๏
๏
๏
๏๏๏๏๏๏๏ซ๏๏๏๏๏๏๏๏๏จ๏๏๏๏ ๏๏๏๏๏๏๏๏
๏๏ฆ
๏๏๏๏๏๏ ๏๏๏๏๏๏๏๏ ๏๏๏ ๏ ๏๏ก๏๏ข๏ ๏ฃ๏ ๏๏ค๏๏๏ข๏
๏๏๏๏๏๏๏๏๏๏๏๏ ๏๏ ๏๏๏ก๏๏ข๏ฃ๏๏ค๏๏๏ฅ๏๏๏ฃ๏
๏๏๏๏๏๏
๏๏๏๏๏๏๏๏ค๏๏๏ค๏๏๏๏ ๏จ๏๏๏๏ค๏๏๏๏ข๏ค๏๏๏๏๏๏ ๏ ๏๏๏๏๏
๏๏ข๏๏๏ก๏๏๏๏ข๏๏๏๏ก ๏๏๏๏๏๏๏ฃ๏๏๏๏ก๏๏๏ข๏
๏ฅ๏๏ข๏ค๏๏๏๏๏๏๏๏
๏๏๏๏๏๏๏๏๏๏ ๏๏๏๏๏ ๏๏๏
๏๏๏๏๏๏๏๏๏๏๏ ๏๏๏ ๏๏ ๏๏๏๏๏๏๏๏ ๏๏๏๏ ๏๏๏๏๏ ๏๏๏๏๏๏๏๏ ๏ ๏๏๏๏ ๏๏๏๏๏๏๏
๏๏๏๏๏๏๏ ๏๏
๏๏๏๏๏
๏ค๏
๏๏๏๏๏
๏๏๏๏๏๏๏๏๏
๏๏๏๏๏๏๏ ๏๏๏๏๏๏
๏๏
๏๏๏๏๏๏๏๏๏๏๏๏๏ข ๏๏๏๏๏๏๏๏๏๏ ๏๏๏
๏ค๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏ฅ๏๏ ๏๏๏๏๏๏๏ข๏๏๏๏๏๏๏๏ก๏๏๏๏๏๏๏ ๏๏๏๏๏๏๏ฆ๏๏๏๏๏๏ฎ ๏๏ช๏๏๏๏๏๏๏๏๏๏ซ๏๏ค๏๏๏๏๏๏๏ ๏๏๏๏๏๏๏
๏ฅ๏๏ข๏ค๏๏๏๏๏๏๏๏
๏ข๏๏๏๏๏๏๏๏ก๏๏๏๏๏๏ ๏ช๏๏ ๏๏๏ข๏๏๏๏ ๏๏๏๏๏๏ฆ๏๏๏ง๏๏
๏ฅ
๏๏๏๏๏๏๏ฆ๏๏๏๏๏๏ฎ ๏๏ช๏๏๏๏๏๏๏๏๏๏ซ๏๏ค๏๏๏๏๏๏๏ ๏๏๏๏๏๏๏
๏ฅ๏๏๏๏ฏ๏๏ค๏๏๏๏๏
๏๏ฆ
๏๏๏๏๏
๏
๏ ๏๏๏๏๏
๏
๏๏
๏ค๏ก๏๏ซ๏๏๏๏ฃ๏๏๏๏๏ฃ๏๏๏๏๏ ๏๏๏๏๏๏๏ซ๏๏๏๏๏๏๏๏๏จ๏๏๏๏ ๏๏๏๏๏๏๏๏๏ค๏๏๏๏๏ ๏๏๏๏๏๏๏๏
๏๏๏๏๏
๏๏
๏๏๏๏ฌ๏๏ ๏๏๏๏๏๏๏๏๏๏ข๏๏ ๏ ๏๏๏๏๏๏๏๏๏๏๏๏๏๏
๏
๏๏๏๏๏๏ ๏๏๏๏๏๏๏๏๏ ๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏ ๏๏๏๏๏๏
๏ ๏๏๏๏๏
๏
๏๏
๏๏ ๏๏๏๏
๏๏๏๏๏
๏
๏๏๏๏๏๏๏๏๏
๏๏
๏๏
๏ค๏๏๏๏๏๏๏๏๏๏๏๏๏๏ ๏ฅ
๏๏๏๏๏๏๏๏ก๏๏
๏๏๏๏๏๏ ๏๏๏๏๏๏๏๏๏ ๏๏๏๏ ๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏ ๏๏๏๏๏๏
๏๏ฉ
๏๏ฉ ๏๏ ๏๏๏
๏ช๏
๏๏๏๏๏๏
๏๏
๏๏๏๏๏๏๏๏๏๏๏๏๏ ๏ ๏๏๏๏๏๏๏ ๏๏๏๏๏๏๏๏๏๏๏๏๏ ๏ ๏ ๏๏๏๏๏๏๏ก๏๏๏๏๏๏ข๏ฃ๏๏๏ข๏ ๏ ๏๏๏๏ ๏ข๏๏๏๏๏ ๏๏๏๏๏๏๏
๏ ๏ฉ ๏๏๏๏
๏ฅ๏๏๏ฏ๏๏๏๏๏๏ข๏๏ฐ๏๏๏๏๏๏๏๏
๏๏
๏๏๏๏๏๏๏๏๏๏๏๏๏
๏๏
๏๏๏๏๏๏
๏๏๏๏๏
๏๏๏๏๏
๏๏๏๏๏๏๏๏๏๏ ๏๏๏๏๏๏๏๏๏
๏๏๏๏๏
๏๏๏ ๏ ๏๏๏๏๏๏๏ ๏ ๏ ๏ฉ ๏ ๏
๏ ๏
๏๏๏๏
๏
๏๏๏๏
๏
๏
๏๏๏
๏๏๏
๏
๏ ๏
๏๏
๏๏๏๏ ๏๏๏๏๏๏๏๏ ๏๏๏๏๏๏๏ ๏ฅ๏ ๏๏๏๏๏๏ ๏๏๏๏๏๏๏๏๏ฆ๏ ๏๏๏๏๏ ๏๏๏๏
๏๏ค ๏ ๏๏ ๏๏ ๏๏ก๏ ๏ข๏ ๏๏ฃ ๏๏๏ก๏ ๏๏๏ ๏๏๏ ๏
๏
๏
๏๏๏๏
๏
๏๏๏๏๏ก๏ข๏๏ฃ๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏
๏๏ ๏๏๏๏
๏
๏
๏
๏๏ค
๏๏๏๏ ๏๏๏๏๏๏๏๏ ๏๏๏๏๏๏๏ ๏ฅ๏ ๏๏๏๏๏๏ ๏๏๏๏๏๏๏๏๏ฆ๏ ๏๏๏๏๏ ๏ง๏๏๏๏๏๏๏
๏ ๏๏ ๏๏ ๏๏ก๏ ๏ข๏ ๏๏ฃ๏๏๏ก๏
๏
๏
๏
๏๏๏๏๏๏ ๏๏ ๏๏๏๏๏๏๏ ๏๏๏
๏๏๏๏
๏๏ฉ
๏
๏๏ค
๏๏๏ ๏๏๏
๏๏๏๏
๏ ๏๏ ๏๏ ๏๏ก๏ ๏ข๏ ๏
๏ค๏ ๏๏๏๏๏๏๏๏๏๏ ๏๏๏๏๏๏
๏๏๏๏๏ ๏๏๏๏๏ ๏
๏๏๏๏๏๏๏๏๏๏๏๏๏ ๏ ๏ฉ ๏๏๏๏ ๏๏ฉ ๏๏๏๏
๏๏ ๏๏๏๏
๏๏๏๏๏๏
๏๏ ๏๏๏๏๏๏๏๏
๏๏ ๏ฅ
๏
๏
๏
๏
๏
๏
๏
๏
๏
๏ค๏๏๏๏๏๏๏๏๏๏ข๏๏ ๏ฅ๏๏ข๏ค๏๏๏๏๏๏๏๏
๏๏ข
๏๏๏๏๏๏๏๏๏๏๏๏ ๏๏ ๏๏๏ก๏๏ข๏ฃ๏๏ค๏๏๏ฅ๏๏๏ฃ๏
๏๏๏๏๏๏๏ ๏๏๏๏๏๏
๏ฅ
๏
๏๏
๏๏๏๏๏๏๏๏ค๏๏๏ค๏๏๏๏ ๏จ๏๏๏๏ค๏๏๏๏ข๏ค๏๏๏๏๏๏ ๏ ๏๏๏๏๏
๏๏
๏๏๏๏๏๏
๏๏ข๏๏๏ก๏๏๏๏ข๏๏๏๏ก ๏๏๏๏๏๏๏ฃ๏๏๏๏ก๏๏๏ข๏
๏ ๏๏๏๏๏ ๏ ๏ ๏
๏๏ ๏๏
๏๏๏ก
๏
๏๏๏๏๏๏๏๏๏
๏๏๏๏
๏๏๏๏๏๏
๏๏ ๏๏ ๏๏๏ ๏
๏
๏
๏๏๏๏๏๏๏๏๏๏ ๏๏๏๏๏๏
๏๏๏ ๏๏๏ ๏ข๏๏๏๏๏๏๏๏ก๏๏๏๏๏๏๏๏๏๏๏๏
๏๏๏
๏
๏
๏๏
๏๏
๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏ ๏๏๏๏ ๏ก๏๏๏๏๏๏ข๏ฃ๏๏๏ข๏ ๏ ๏ข๏๏๏๏๏ ๏๏๏๏๏๏๏
๏๏๏๏๏๏
๏ ๏
๏๏๏
๏๏๏๏๏
๏ ๏๏๏๏๏
๏ ๏
๏๏๏๏๏๏๏๏๏๏๏๏๏
๏๏๏๏๏๏ ๏๏๏๏๏๏๏๏ ๏๏๏ ๏ ๏๏๏๏๏๏๏ ๏๏๏ ๏๏
๏ ๏๏ก๏๏ข๏ ๏ฃ๏ ๏๏ค๏๏๏ข๏
๏๏๏๏๏
๏ ๏๏๏๏๏
๏ ๏ ๏ ๏
๏๏
๏๏๏๏๏๏๏๏๏๏๏๏๏ข ๏๏๏๏๏ก๏ข๏๏ฃ๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏ ๏๏๏๏๏๏๏๏๏๏ ๏๏๏
๏๏๏๏ญ๏๏๏๏๏
๏ ๏
๏๏ ๏๏๏๏
๏๏๏๏๏
๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏
๏๏
๏๏๏๏๏๏๏๏ ๏๏๏๏๏๏๏ ๏ฅ๏ ๏๏๏๏๏๏ ๏๏๏๏๏๏๏๏๏ฆ๏ ๏๏๏๏๏ ๏๏๏๏ ๏ ๏๏ ๏๏ ๏๏ก๏ ๏ข๏ ๏๏ฃ๏๏๏ก๏
๏๏ ๏๏๏๏
๏๏๏๏๏๏
๏๏๏๏๏๏ฅ๏๏๏ ๏๏๏๏๏๏ ๏๏๏๏ ๏ ๏๏ก๏๏ข๏ ๏ฃ๏ ๏๏ค๏๏๏ข๏
๏๏๏๏ ๏๏๏๏๏๏๏๏๏๏๏๏๏ข๏๏๏๏ ๏๏๏๏ข๏๏ฆ๏๏๏ ๏๏๏๏๏๏๏๏๏๏๏๏ค๏๏
๏ค๏๏๏๏๏๏๏๏๏๏๏๏๏๏
๏๏๏๏๏๏
๏๏ฉ
๏๏๏๏ ๏ ๏๏ก๏ ๏ข๏ ๏๏ฃ๏๏๏ก๏
๏ ๏๏๏ค๏๏
๏๏๏๏
๏๏๏๏๏
๏๏๏๏
๏๏ค
๏ข๏๏๏
๏๏๏๏๏๏
๏๏๏๏
๏๏๏ข๏๏๏๏ ๏๏
๏๏
๏๏๏๏๏๏๏๏๏๏๏๏๏ข ๏๏๏๏๏๏๏๏๏๏ ๏๏๏ ๏๏๏๏ ๏๏๏๏
๏๏
๏๏๏๏๏๏ ๏๏๏๏๏๏๏๏๏ ๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏ ๏๏๏๏๏๏
๏๏๏๏๏๏ ๏๏๏
๏๏๏๏๏
๏๏๏๏ฉ๏๏๏๏๏
๏๏๏๏๏๏๏ฆ๏๏๏๏๏๏ฎ ๏๏ช๏๏๏๏๏๏๏๏๏๏ซ๏๏ค๏๏๏๏๏๏๏ ๏๏๏๏๏๏๏
๏๏๏๏๏๏๏๏๏
๏๏๏๏๏
๏๏๏๏๏๏ฉ๏๏๏
๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏ ๏๏๏๏๏
๏๏๏๏๏๏๏๏๏๏๏ ๏๏๏๏๏๏๏ ๏๏๏ค๏๏๏๏ ๏๏
๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏ ๏ก๏๏๏๏๏๏ข๏ฃ๏๏๏ข๏ ๏ ๏ข๏๏๏๏๏ ๏๏๏๏๏๏๏
๏๏๏๏๏
๏ ๏๏๏๏๏๏๏
๏๏๏๏๏๏ ๏ช๏๏
๏๏๏๏๏
๏๏
๏๏๏๏๏๏๏๏๏๏๏๏๏ฅ๏๏
๏๏๏๏๏๏๏๏๏๏๏๏๏ข ๏๏๏๏๏๏๏๏๏๏ ๏๏๏ ๏ ๏๏๏๏๏๏๏๏๏๏ข๏๏ฅ๏๏๏๏
๏๏๏๏๏๏๏ก๏๏
๏๏๏๏
๏๏๏๏๏๏๏ซ๏๏๏๏๏๏๏๏๏จ๏๏๏๏ ๏๏๏๏๏๏๏๏
๏ ๏๏๏๏๏๏๏๏๏๏ข๏๏ฅ๏๏๏๏ ๏ ๏๏๏๏๏๏๏ ๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏
๏๏๏๏๏
๏๏๏๏๏๏๏ฆ๏๏๏๏๏๏ฎ ๏๏ ๏๏ช๏๏๏๏๏๏๏๏๏๏ซ๏๏ค๏๏๏๏๏๏๏ ๏๏๏ ๏ ๏๏๏๏๏๏๏
๏๏๏
๏๏๏๏๏๏๏
๏ค๏ฃ๏ก๏๏๏ค๏๏๏๏๏๏๏๏ ๏๏๏๏จ๏
๏ช๏๏
๏๏
๏๏๏๏๏
๏๏
๏ฅ๏๏๏๏ฏ๏๏ค๏๏๏๏๏
๏๏๏
๏๏๏๏๏๏๏๏๏๏๏ข๏๏๏๏
๏๏๏ก ๏๏๏๏๏๏๏๏
๏๏๏ ๏
๏๏ ๏๏๏ ๏๏๏ ๏๏๏ ๏๏ ๏๏๏
๏๏๏ ๏๏
๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏ ๏๏๏๏
๏๏๏๏๏
๏๏๏๏๏๏๏ซ๏๏๏๏๏๏๏๏๏จ๏๏๏๏
๏๏
๏๏๏๏๏๏
๏๏๏๏๏ฅ ๏๏๏๏๏๏๏๏๏๏๏ ๏๏๏๏๏๏๏ ๏๏๏ ๏๏๏๏๏๏๏๏๏๏ ๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏ก๏๏๏๏๏๏ข๏ฃ ๏๏ข๏ ๏๏๏ข๏๏๏๏๏ ๏๏๏๏๏๏๏ ๏๏ ๏๏ ๏๏๏ ๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏
๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏ ๏๏๏๏๏๏ ๏๏๏๏๏๏๏๏๏ ๏๏๏๏๏ ๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏ ๏ง๏๏๏ค๏๏๏ค๏ฃ๏๏ง๏๏ ๏๏๏๏๏๏
๏๏๏๏๏
๏๏
๏๏๏๏๏ค๏๏๏
๏๏
๏๏
๏๏ ๏ช๏
๏๏
๏๏๏๏๏๏ ๏๏๏๏๏๏๏๏๏ ๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏ ๏๏๏๏๏๏
๏๏๏๏๏
๏๏
๏๏๏๏๏๏๏๏๏๏๏๏๏ฅ๏๏
๏๏๏๏๏๏๏๏๏
๏๏ ๏ค๏๏๏๏๏๏๏๏๏๏๏๏๏๏ ๏๏๏๏ฌ๏๏ ๏๏๏๏๏๏๏๏๏๏ข๏๏ ๏๏ ๏๏๏๏๏๏๏๏๏๏๏๏๏๏ ๏๏๏ ๏
๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏ ๏ก๏๏๏๏๏๏๏ง๏๏๏๏๏
๏๏๏๏๏๏
๏๏๏๏๏๏
๏๏๏๏๏๏๏ ๏ฅ๏๏๏ฏ๏๏๏๏๏๏ข๏๏ฐ๏๏๏๏๏๏๏๏ ๏๏๏ก
๏๏
๏๏๏ ๏
๏๏
๏๏๏ก
๏๏๏๏๏๏
๏๏ ๏๏๏ ๏
๏๏๏๏ ๏๏๏๏๏ ๏๏๏๏๏๏
๏๏๏๏๏๏๏๏๏๏ ๏๏๏๏ฌ๏๏ ๏๏๏๏๏๏๏๏๏๏ข๏๏ ๏๏๏๏๏๏๏๏๏๏๏๏๏๏
๏ค๏ฃ๏๏ค๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏ฅ ๏ค๏ ๏๏ ๏๏ ๏๏๏ฃ๏๏๏๏๏
๏๏๏๏๏
๏๏๏๏๏๏๏๏๏๏๏๏๏
๏๏๏๏๏ง๏๏๏๏๏๏๏จ๏๏๏๏ ๏๏๏๏ ๏๏๏๏๏ ๏๏๏๏๏ ๏๏๏๏๏๏๏๏๏ฉ๏๏๏ช๏๏๏๏๏๏ ๏๏๏ซ๏๏ค๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏
๏๏
๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏
๏ฅ๏๏๏๏ฏ๏๏ค๏๏๏๏๏
๏๏๏๏ช๏
๏๏๏๏๏
๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏ ๏๏๏๏๏๏๏๏๏๏ ๏๏๏๏๏๏๏๏๏
๏๏ ๏๏๏๏๏๏๏ ๏๏๏๏ ๏๏๏ฅ๏๏ฆ๏๏๏ข
๏๏๏๏ ๏๏๏๏
๏ค๏๏๏๏๏๏๏๏๏๏๏๏๏๏
๏๏๏๏๏๏๏๏๏๏๏๏๏๏ค๏๏๏๏๏๏ฃ๏๏ ๏ค๏๏
๏๏๏๏๏๏ ๏๏
๏๏๏๏๏
๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏ ๏๏๏๏๏๏๏ ๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏ ๏ก๏๏๏๏๏๏ข๏ฃ๏๏๏ข๏ ๏๏๏ข๏๏๏ ๏ ๏๏๏๏๏๏๏
๏๏๏๏
๏๏๏๏
๏๏๏ ๏
๏๏
๏๏
๏๏๏๏๏ง๏๏๏๏๏๏๏จ๏๏๏๏ ๏๏๏๏๏ ๏๏๏๏๏๏๏๏๏ฉ๏๏๏ช๏๏๏๏๏๏ ๏๏๏ซ๏๏ค๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏
๏๏ ๏๏ ๏๏
๏๏
๏๏๏๏๏๏ซ๏๏๏๏๏๏๏๏๏๏ข๏๏๏๏๏๏๏๏๏ข ๏๏๏๏๏๏๏๏
๏๏๏๏๏๏
๏๏๏๏๏๏๏ ๏๏๏๏ ๏๏๏ฅ๏๏ฆ๏๏๏ข
๏๏๏
๏๏ฃ๏๏๏ฃ๏๏๏ค๏ฃ๏๏ค๏๏๏๏ ๏๏๏ก๏๏ค๏ฅ๏๏๏๏ค๏๏๏๏๏ก๏ ๏๏๏๏๏๏
๏๏๏๏๏๏๏๏๏๏๏๏๏
๏๏๏๏
๏๏๏๏ฌ๏๏ ๏๏๏๏๏๏๏๏๏๏ข๏๏ ๏๏๏๏๏๏๏๏๏๏๏๏๏๏
๏๏๏๏๏๏๏๏๏๏๏๏๏ ๏ ๏๏๏๏๏๏๏ ๏๏๏๏๏๏๏๏๏๏๏๏๏ ๏๏๏๏๏๏๏ก๏๏๏๏๏๏ข๏ฃ๏๏๏ข๏ ๏ ๏ข๏๏๏๏๏ ๏๏๏๏๏๏๏
๏๏๏๏๏๏๏๏๏๏ฅ๏๏ฆ๏๏๏ข ๏๏๏๏๏๏๏๏๏๏๏ข๏๏๏๏
๏๏๏๏๏๏
๏๏๏๏๏๏
๏ค๏๏๏๏๏๏๏๏๏๏๏๏๏๏
๏๏
๏๏๏๏๏๏
๏๏๏๏๏๏
๏๏
๏ข๏๏๏๏๏๏๏๏ค๏๏๏๏๏๏๏๏๏๏
๏๏๏๏๏๏๏ข๏๏๏๏๏๏๏๏ก๏๏ค๏๏๏๏๏๏๏๏๏๏ ๏ฅ๏๏ข๏ค๏๏๏๏๏๏๏๏
๏๏๏๏๏๏๏ ๏๏ ๏ฅ๏๏ข๏ค๏๏๏๏๏๏๏๏ ๏ค๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏๏ฅ๏๏
๏๏๏๏๏ ๏๏๏๏๏๏๏๏ ๏๏
๏๏๏๏๏๏ ๏๏๏ ๏ ๏๏๏๏๏๏๏ ๏๏
A4.1
๏๏๏๏๏๏๏๏๏๏๏ ๏๏๏๏๏๏๏๏๏ ๏๏๏๏๏ ๏๏๏๏ ๏๏ ๏๏๏๏ ๏๏๏ ๏๏๏๏๏๏ ๏๏๏ ๏๏๏๏๏ก๏๏๏๏ ๏๏๏๏๏๏๏๏๏ข๏๏๏๏ ๏๏๏๏๏๏ ๏๏๏๏๏๏๏ ๏๏ ๏๏๏๏๏๏๏๏๏๏๏๏๏๏ ๏๏๏๏๏๏ ๏๏๏๏๏๏ ๏๏๏๏๏๏๏ ๏๏๏๏๏๏๏๏๏๏๏ ๏๏๏๏๏๏๏๏ ๏๏๏ ๏๏๏๏๏ ๏๏๏๏๏๏๏๏ ๏๏๏๏๏๏๏๏๏๏๏ฅ
SAMUEL AARON WILLIAMS saw2025@vt.edu 540.808.9874