그림자 구현방법에는 원형 그림자, 투영 그림자, 그리고 깊이 버퍼 그림자 방식이 있다.  이 중 가장 정교한 묘사가 가능한 깊이 버퍼 그림자(Depth Buffer Shadow)를 구현하여 그림자를 표현하였다. Two Pass Rendering 원리를 이용하여 깊이 버퍼 그림자를 계산하고 이를 활용한다. 

 

목차

     

     


     

     

    그림자 구현하기

     

     

    그림자 구현방법

    • 원형 그림자:  고전 방식
    • 투영 그림자:  그 다음 등장한  방식. 장면 그대로 렌더링
    • 깊이 버퍼 그림자 (Depth Buffer Shadow): 최근 대부분의 게임에서 사용하는 방식. 
      • 깊이 버퍼를 이용하여 그림자를 구현한다. 

     

     

    깊이 버퍼 그림자 (Depth Buffer Shadow)

    • Two Pass Rendering
      • 1 Pass: 깊이(DSV) - 조명의 방향을 가지고 Projection 렌더링 진행한다.
        • Light 공간(WVP)
      • 2 Pass: 깊이를 비교해가면서 실제 렌더링을 수행한다. 
        • Main Camera 공간(WVP)
        • Light 공간(WVP)에서 깊이를 비교한다.
          • depth >= z 이면 그림자가 생길 부분이 아니다. 
          • depth < z   이면  그림자가 지어질 영역이다.
      • 여기서 말하는 하나의 패스(Pass)는 IA → VS → RS → PS → OM을 지난다는 것을 의미한다.

     

     

    Shaders
      Render.fx
    Light.fx
    Shadow.fx 생성
    Framework
      Objects
      Shadow.h .cpp 생성
    UnitTest
      Objects
      ShadowDemo.h .cpp 생성

     

     


     

     

    Render.fx

     

    Render.fx

    더보기
    struct DepthOutput
    {
    float4 Position : SV_Position;
    float4 sPosition : Position1;
    };
    float4 PS_Depth(DepthOutput input) : SV_Target
    {
    float depth = input.Position.z / input.Position.w;
    return float4(depth, depth, depth, 1.0f);
    }
    #define VS_DEPTH_GENERATE \
    output.Position = WorldPosition(input.Position); \
    output.Position = mul(output.Position, ShadowView); \
    output.Position = mul(output.Position, ShadowProjection); \
    \
    output.sPosition = output.Position;
    DepthOutput VS_Depth_Mesh(VertexMesh input)
    {
    DepthOutput output;
    SetMeshWorld(World, input);
    VS_DEPTH_GENERATE
    return output;
    }
    DepthOutput VS_Depth_Model(VertexModel input)
    {
    DepthOutput output;
    SetModelWorld(World, input);
    VS_DEPTH_GENERATE
    return output;
    }
    DepthOutput VS_Depth_Animation(VertexModel input)
    {
    DepthOutput output;
    if (BlendFrames[input.InstanceID].Mode == 0)
    SetTweenWorld(World, input);
    else
    SetBlendWorld(World, input);
    VS_DEPTH_GENERATE
    return output;
    }

     

     


     

     

     

    Light.fx

     

    Light.fx

    더보기
    cbuffer CB_Shadow
    {
    matrix ShadowView;
    matrix ShadowProjection;
    float2 ShadowMapSize;
    float ShadowBias;
    uint ShadowQuality;
    };

     

     


     

     

    Shadow.fx

     

    Shadow.fx

    #include "00_Global.fx"
    #include "00_Light.fx"
    #include "00_Render.fx"
    float4 PS(MeshOutput input) : SV_Target
    {
    //float4 color = float4(1, 1, 1, 1);
    float4 color = PS_AllLight(input);
    float4 position = input.sPosition;
    position.xyz /= position.w;
    [flatten]
    if (position.x < -1.0f || position.x > +1.0f ||
    position.y < -1.0f || position.y > +1.0f ||
    position.z < +0.0f || position.z > +1.0f)
    {
    return color;
    }
    position.x = position.x * 0.5f + 0.5f;
    position.y = -position.y * 0.5f + 0.5f;
    float depth = 0;
    float z = position.z - ShadowBias;
    float factor = 0;
    if(ShadowQuality == 0)
    {
    depth = ShadowMap.Sample(LinearSampler, position.xy).r;
    factor = (float) (depth >= z);
    }
    else if (ShadowQuality == 1) //PCF
    {
    depth = position.z;
    factor = ShadowMap.SampleCmpLevelZero(ShadowSampler, position.xy, depth).r;
    }
    else if (ShadowQuality == 2) //PCF + Blur
    {
    depth = position.z;
    float2 size = 1.0f / ShadowMapSize;
    float2 offsets[] =
    {
    float2(-size.x, -size.y), float2(0.0f, -size.y), float2(+size.x, -size.y),
    float2(-size.x, 0.0f), float2(0.0f, 0.0f), float2(+size.x, 0.0f),
    float2(-size.x, +size.y), float2(0.0f, +size.y), float2(+size.x, +size.y),
    };
    float2 uv = 0;
    float sum = 0;
    [unroll(9)]
    for (int i = 0; i < 9; i++)
    {
    uv = position.xy + offsets[i];
    sum += ShadowMap.SampleCmpLevelZero(ShadowSampler, uv, depth).r;
    }
    factor = sum / 9.0f;
    }
    factor = saturate(factor + depth);
    return color * factor;
    }
    technique11 T0
    {
    //1Pass - Depth Rendering
    //P_VP(P0, VS_Depth_Mesh, PS_Depth)
    //P_VP(P1, VS_Depth_Model, PS_Depth)
    //P_VP(P2, VS_Depth_Animation, PS_Depth)
    //1Pass - Depth Rendering
    //z-fighting 문제가 발생하지 않도록 뒤집어(P_RS_VP)준다.
    P_RS_VP(P0, FrontCounterClockwise_True, VS_Depth_Mesh, PS_Depth)
    P_RS_VP(P1, FrontCounterClockwise_True, VS_Depth_Model, PS_Depth)
    P_RS_VP(P2, FrontCounterClockwise_True, VS_Depth_Animation, PS_Depth)
    P_VP(P3, VS_Mesh, PS)
    P_VP(P4, VS_Model, PS)
    P_VP(P5, VS_Animation, PS)
    }

     

    z-fighting 문제가 발생하지 않도록 뒤집어(P_RS_VP, FrontCounterClockwise)준다.

    • technique11 T0 {
          //1Pass - Depth Rendering
          P_RS_VP(P0, FrontCounterClockwise_True, VS_Depth_Mesh, PS_Depth)
          P_RS_VP(P1, FrontCounterClockwise_True, VS_Depth_Model, PS_Depth)
          P_RS_VP(P2, FrontCounterClockwise_True, VS_Depth_Animation, PS_Depth) }

     

     

    Shadow

     

    Shadow.h

    더보기
    #pragma once
    class Shadow
    {
    public:
    Shadow(Shader* shader, Vector3& position, float radius, UINT width = 1024, UINT height = 1024);
    ~Shadow();
    void PreRender();
    ID3D11ShaderResourceView* SRV() { return renderTarget->SRV(); }
    private:
    void CalcViewProjection();
    private:
    struct Desc
    {
    Matrix View;//그림자를 그리기 위한 빛 방향에서의 View Projection
    Matrix Projection;
    Vector2 MapSize;
    float Bias = -0.0006f;
    UINT Quality = 0;
    } desc;
    private:
    Shader* shader;
    UINT width, height;//그림자 맵의 해상도를 결정한 너비와 높이
    Vector3 position;//조명이 빛을 비출 위치
    float radius;//조명 구역. 그림자가 들어갈 구역.
    RenderTarget* renderTarget;
    DepthStencil* depthStencil;
    Viewport* viewport;
    ConstantBuffer* buffer;
    ID3DX11EffectConstantBuffer* sBuffer;//그림자 정보 넘길 변수
    ID3DX11EffectShaderResourceVariable* sShadowMap;//깊이를 줄 변수
    ID3D11SamplerState* pcfSampler;
    ID3DX11EffectSamplerVariable* sPcfSampler;
    };

     

     

     

    Shadow.cpp

    더보기
    #include "Framework.h"
    #include "Shadow.h"
    Shadow::Shadow(Shader * shader, Vector3 & position, float radius, UINT width, UINT height)
    : shader(shader), position(position), radius(radius), width(width), height(height)
    {
    renderTarget = new RenderTarget(width, height);
    depthStencil = new DepthStencil(width, height);
    viewport = new Viewport((float)width, (float)height);
    desc.MapSize = Vector2((float)width, (float)height);
    buffer = new ConstantBuffer(&desc, sizeof(Desc));
    sBuffer = shader->AsConstantBuffer("CB_Shadow");
    sShadowMap = shader->AsSRV("ShadowMap");
    //Create Sampler State
    {
    D3D11_SAMPLER_DESC desc;
    ZeroMemory(&desc, sizeof(D3D11_SAMPLER_DESC));
    desc.Filter = D3D11_FILTER_COMPARISON_MIN_MAG_MIP_LINEAR;
    desc.ComparisonFunc = D3D11_COMPARISON_LESS_EQUAL;
    desc.AddressU = D3D11_TEXTURE_ADDRESS_CLAMP;
    desc.AddressV = D3D11_TEXTURE_ADDRESS_CLAMP;
    desc.AddressW = D3D11_TEXTURE_ADDRESS_CLAMP;
    desc.MaxAnisotropy = 1;
    desc.MaxLOD = FLT_MAX;
    Check(D3D::GetDevice()->CreateSamplerState(&desc, &pcfSampler));
    sPcfSampler = shader->AsSampler("ShadowSampler");
    }
    }
    Shadow::~Shadow()
    {
    SafeDelete(renderTarget);
    SafeDelete(depthStencil);
    SafeDelete(viewport);
    SafeDelete(buffer);
    }
    void Shadow::PreRender()
    {
    ImGui::InputInt("Quality", (int *)&desc.Quality);
    desc.Quality %= 3;
    //1Pass
    ImGui::SliderFloat3("Light Direction", Context::Get()->Direction(), -1, +1);
    ImGui::SliderFloat("Bias", &desc.Bias, -0.0001f, +0.01f, "%.4f");
    renderTarget->PreRender(depthStencil);
    viewport->RSSetViewport();
    CalcViewProjection();
    buffer->Render();
    sBuffer->SetConstantBuffer(buffer->Buffer());
    sShadowMap->SetResource(depthStencil->SRV());
    sPcfSampler->SetSampler(0, pcfSampler);
    }
    void Shadow::CalcViewProjection()
    {
    Vector3 up = Vector3(0, 1, 0);
    Vector3 direction = Context::Get()->Direction();//주 빛의 방향(=조명 방향)
    Vector3 position = direction * radius * -2.0f;//
    D3DXMatrixLookAtLH(&desc.View, &position, &this->position, &up);
    Vector3 origin;
    D3DXVec3TransformCoord(&origin, &this->position, &desc.View);//원점을 View공간 만큼 움직인다.
    float l = origin.x - radius;
    float b = origin.y - radius;
    float n = origin.z - radius;
    float r = origin.x + radius;
    float t = origin.y + radius;
    float f = origin.z + radius;
    D3DXMatrixOrthoLH(&desc.Projection, r - l, t - b, n, f);
    }

     

     


     

     

    ShadowDemo

     

    ShadowDemo.h

    더보기
    #pragma once
    #include "Systems/IExecute.h"
    class ShadowDemo : public IExecute
    {
    public:
    virtual void Initialize() override;
    virtual void Ready() override {}
    virtual void Destroy() override {}
    virtual void Update() override;
    virtual void PreRender() override;
    virtual void Render() override;
    virtual void PostRender() override;
    virtual void ResizeScreen() override {}
    private:
    void Mesh();
    void Airplane();
    void Kachujin();
    void KachujinCollider();
    void KachujinWeapon();
    void PointLighting();
    void SpotLighting();
    void Pass(UINT mesh, UINT model, UINT anim);
    private:
    Shader* shader;
    Shadow* shadow;
    Render2D* render2D;
    CubeSky* sky;
    Material* floor;
    Material* stone;
    Material* brick;
    Material* wall;
    MeshRender* cube;
    MeshRender* cylinder;
    MeshRender* sphere;
    MeshRender* grid;
    ModelRender* airplane = NULL;
    ModelAnimator* kachujin = NULL;
    Transform* colliderInitTransforms;
    ColliderObject** colliders;
    ModelRender* weapon = NULL;
    Transform* weaponInitTransform;
    vector<MeshRender *> meshes;
    vector<ModelRender *> models;
    vector<ModelAnimator *> animators;
    };

     

     

     

    ShadowDemo.cpp

    더보기
    #include "stdafx.h"
    #include "ShadowDemo.h"
    void ShadowDemo::Initialize()
    {
    Context::Get()->GetCamera()->RotationDegree(20, 0, 0);
    Context::Get()->GetCamera()->Position(1, 36, -85);
    ((Freedom *)Context::Get()->GetCamera())->Speed(50, 2);
    shader = new Shader(L"113_Shadow.fxo");
    UINT size = 1024;// * 8; * 16;
    shadow = new Shadow(shader, Vector3(0, 0, 0), 65, size, size);
    render2D = new Render2D();
    //render2D->GetTransform()->Position(D3D::Width() * 0.5f, D3D::Height() * 0.5f, 0);
    //render2D->GetTransform()->Scale(D3D::Width(), D3D::Height(), 1);
    render2D->GetTransform()->Position(150, D3D::Height() - 150, 0);
    render2D->GetTransform()->Scale(300, 300, 1);
    render2D->SRV(shadow->SRV());
    sky = new CubeSky(L"Environment/GrassCube1024.dds");
    Mesh();
    Airplane();
    Kachujin();
    KachujinCollider();
    KachujinWeapon();
    PointLighting();
    SpotLighting();
    }
    void ShadowDemo::Update()
    {
    sky->Update();
    cube->Update();
    grid->Update();
    cylinder->Update();
    sphere->Update();
    airplane->Update();
    kachujin->Update();
    Matrix worlds[MAX_MODEL_TRANSFORMS];
    for (UINT i = 0; i < kachujin->GetTransformCount(); i++)
    {
    kachujin->GetAttachTransform(i, worlds);
    weapon->GetTransform(i)->World(weaponInitTransform->World() * worlds[40]);
    }
    weapon->UpdateTransforms();
    weapon->Update();
    render2D->Update();
    }
    void ShadowDemo::PreRender()
    {
    shadow->PreRender();
    Pass(0, 1, 2);
    wall->Render();
    sphere->Render();
    brick->Render();
    cylinder->Render();
    stone->Render();
    cube->Render();
    floor->Render();
    grid->Render();
    airplane->Render();
    kachujin->Render();
    weapon->Render();
    }
    void ShadowDemo::Render()
    {
    sky->Pass(0);
    sky->Render();
    Pass(3, 4, 5);
    wall->Render();
    sphere->Render();
    brick->Render();
    cylinder->Render();
    stone->Render();
    cube->Render();
    floor->Render();
    grid->Render();
    airplane->Render();
    kachujin->Render();
    weapon->Render();
    }
    void ShadowDemo::PostRender()
    {
    render2D->Render();
    }
    void ShadowDemo::Mesh()
    {
    //Create Material
    {
    floor = new Material(shader);
    floor->DiffuseMap("Floor.png");
    floor->Specular(1, 1, 1, 20);
    floor->SpecularMap("Floor_Specular.png");
    floor->NormalMap("Floor_Normal.png");
    stone = new Material(shader);
    stone->DiffuseMap("Stones.png");
    stone->Specular(1, 1, 1, 20);
    stone->SpecularMap("Stones_Specular.png");
    stone->Emissive(0.15f, 0.15f, 0.15f, 0.3f);
    stone->NormalMap("Stones_Normal.png");
    brick = new Material(shader);
    brick->DiffuseMap("Bricks.png");
    brick->Specular(1, 0.3f, 0.3f, 20);
    brick->SpecularMap("Bricks_Specular.png");
    brick->Emissive(0.15f, 0.15f, 0.15f, 0.3f);
    brick->NormalMap("Bricks_Normal.png");
    wall = new Material(shader);
    wall->DiffuseMap("Wall.png");
    wall->Specular(1, 1, 1, 20);
    wall->SpecularMap("Wall_Specular.png");
    wall->Emissive(0.15f, 0.15f, 0.15f, 0.3f);
    wall->NormalMap("Wall_Normal.png");
    }
    //Create Mesh
    {
    Transform* transform = NULL;
    cube = new MeshRender(shader, new MeshCube());
    transform = cube->AddTransform();
    transform->Position(0, 5, 0);
    transform->Scale(20, 10, 20);
    grid = new MeshRender(shader, new MeshGrid(5, 5));
    transform = grid->AddTransform();
    transform->Position(0, 0, 0);
    transform->Scale(12, 1, 12);
    cylinder = new MeshRender(shader, new MeshCylinder(0.5f, 3.0f, 20, 20));
    sphere = new MeshRender(shader, new MeshSphere(0.5f, 20, 20));
    for (UINT i = 0; i < 5; i++)
    {
    transform = cylinder->AddTransform();
    transform->Position(-30, 6, -15.0f + (float)i * 15.0f);
    transform->Scale(5, 5, 5);
    transform = cylinder->AddTransform();
    transform->Position(30, 6, -15.0f + (float)i * 15.0f);
    transform->Scale(5, 5, 5);
    transform = sphere->AddTransform();
    transform->Position(-30, 15.5f, -15.0f + (float)i * 15.0f);
    transform->Scale(5, 5, 5);
    transform = sphere->AddTransform();
    transform->Position(30, 15.5f, -15.0f + (float)i * 15.0f);
    transform->Scale(5, 5, 5);
    }
    }
    sphere->UpdateTransforms();
    cylinder->UpdateTransforms();
    cube->UpdateTransforms();
    grid->UpdateTransforms();
    meshes.push_back(sphere);;
    meshes.push_back(cylinder);
    meshes.push_back(cube);
    meshes.push_back(grid);
    }
    void ShadowDemo::Airplane()
    {
    airplane = new ModelRender(shader);
    airplane->ReadMesh(L"B787/Airplane");
    airplane->ReadMaterial(L"B787/Airplane");
    Transform* transform = airplane->AddTransform();
    transform->Position(2.0f, 9.91f, 2.0f);
    transform->Scale(0.004f, 0.004f, 0.004f);
    airplane->UpdateTransforms();
    models.push_back(airplane);
    }
    void ShadowDemo::Kachujin()
    {
    kachujin = new ModelAnimator(shader);
    kachujin->ReadMesh(L"Kachujin/Mesh");
    kachujin->ReadMaterial(L"Kachujin/Mesh");
    kachujin->ReadClip(L"Kachujin/Sword And Shield Idle");
    kachujin->ReadClip(L"Kachujin/Sword And Shield Walk");
    kachujin->ReadClip(L"Kachujin/Sword And Shield Run");
    kachujin->ReadClip(L"Kachujin/Sword And Shield Slash");
    kachujin->ReadClip(L"Kachujin/Salsa Dancing");
    Transform* transform = NULL;
    transform = kachujin->AddTransform();
    transform->Position(0, 0, -30);
    transform->Scale(0.075f, 0.075f, 0.075f);
    kachujin->PlayTweenMode(0, 0, 1.0f);
    transform = kachujin->AddTransform();
    transform->Position(-15, 0, -30);
    transform->Scale(0.075f, 0.075f, 0.075f);
    kachujin->PlayTweenMode(1, 1, 1.0f);
    transform = kachujin->AddTransform();
    transform->Position(-30, 0, -30);
    transform->Scale(0.075f, 0.075f, 0.075f);
    kachujin->PlayTweenMode(2, 2, 0.75f);
    transform = kachujin->AddTransform();
    transform->Position(15, 0, -30);
    transform->Scale(0.075f, 0.075f, 0.075f);
    kachujin->PlayBlendMode(3, 0, 1, 2);
    kachujin->SetBlendAlpha(3, 1.5f);
    transform = kachujin->AddTransform();
    transform->Position(30, 0, -32.5f);
    transform->Scale(0.075f, 0.075f, 0.075f);
    kachujin->PlayTweenMode(4, 4, 0.75f);
    kachujin->UpdateTransforms();
    animators.push_back(kachujin);
    }
    void ShadowDemo::KachujinCollider()
    {
    UINT count = kachujin->GetTransformCount();
    colliders = new ColliderObject*[count];
    colliderInitTransforms = new Transform();
    colliderInitTransforms->Position(-2.9f, 1.45f, -50.0f);
    colliderInitTransforms->Scale(5, 5, 75);
    for (UINT i = 0; i < count; i++)
    {
    colliders[i] = new ColliderObject();
    //colliders[i]->Init = new Transform();
    //colliders[i]->Init->Position(0, 0, 0);
    //colliders[i]->Init->Scale(10, 30, 10);
    colliders[i]->Transform = new Transform();
    //colliders[i]->Collider = new Collider(colliders[i]->Transform, colliders[i]->Init);
    colliders[i]->Collider = new Collider(colliders[i]->Transform, colliderInitTransforms);
    }
    }
    void ShadowDemo::KachujinWeapon()
    {
    weapon = new ModelRender(shader);
    weapon->ReadMesh(L"Weapon/Sword");
    weapon->ReadMaterial(L"Weapon/Sword");
    UINT count = kachujin->GetTransformCount();
    for (UINT i = 0; i < count; i++)
    weapon->AddTransform();
    weapon->UpdateTransforms();
    models.push_back(weapon);
    weaponInitTransform = new Transform();
    weaponInitTransform->Position(-2.9f, 1.45f, -6.45f);
    weaponInitTransform->Scale(0.5f, 0.5f, 0.75f);
    weaponInitTransform->Rotation(0, 0, 1);
    }
    void ShadowDemo::PointLighting()
    {
    PointLight light;
    light =
    {
    Color(0.0f, 0.0f, 0.0f, 1.0f), //Ambient
    Color(0.0f, 0.0f, 1.0f, 1.0f), //Diffuse
    Color(0.0f, 0.0f, 0.7f, 1.0f), //Specular
    Color(0.0f, 0.0f, 0.7f, 1.0f), //Emissive
    Vector3(-30, 10, -30), 5.0f, 0.9f
    };
    Lighting::Get()->AddPointLight(light);
    light =
    {
    Color(0.0f, 0.0f, 0.0f, 1.0f),
    Color(1.0f, 0.0f, 0.0f, 1.0f),
    Color(0.6f, 0.2f, 0.0f, 1.0f),
    Color(0.6f, 0.3f, 0.0f, 1.0f),
    Vector3(15, 10, -30), 10.0f, 0.3f
    };
    Lighting::Get()->AddPointLight(light);
    light =
    {
    Color(0.0f, 0.0f, 0.0f, 1.0f), //Ambient
    Color(0.0f, 1.0f, 0.0f, 1.0f), //Diffuse
    Color(0.0f, 0.7f, 0.0f, 1.0f), //Specular
    Color(0.0f, 0.7f, 0.0f, 1.0f), //Emissive
    Vector3(-5, 1, -17.5f), 5.0f, 0.9f
    };
    Lighting::Get()->AddPointLight(light);
    light =
    {
    Color(0.0f, 0.0f, 0.0f, 1.0f),
    Color(0.0f, 0.0f, 1.0f, 1.0f),
    Color(0.0f, 0.0f, 0.7f, 1.0f),
    Color(0.0f, 0.0f, 0.7f, 1.0f),
    Vector3(-10, 1, -17.5f), 5.0f, 0.9f
    };
    Lighting::Get()->AddPointLight(light);
    }
    void ShadowDemo::SpotLighting()
    {
    SpotLight light;
    light =
    {
    Color(0.3f, 1.0f, 0.0f, 1.0f),
    Color(0.7f, 1.0f, 0.0f, 1.0f),
    Color(0.3f, 1.0f, 0.0f, 1.0f),
    Color(0.3f, 1.0f, 0.0f, 1.0f),
    Vector3(-15, 20, -30), 25.0f,
    Vector3(0, -1, 0), 30.0f, 0.4f
    };
    Lighting::Get()->AddSpotLight(light);
    light =
    {
    Color(1.0f, 0.2f, 0.9f, 1.0f),
    Color(1.0f, 0.2f, 0.9f, 1.0f),
    Color(1.0f, 0.2f, 0.9f, 1.0f),
    Color(1.0f, 0.2f, 0.9f, 1.0f),
    Vector3(0, 20, -30), 30.0f,
    Vector3(0, -1, 0), 40.0f, 0.55f
    };
    Lighting::Get()->AddSpotLight(light);
    }
    void ShadowDemo::Pass(UINT mesh, UINT model, UINT anim)
    {
    for (MeshRender* temp : meshes)
    temp->Pass(mesh);
    for (ModelRender* temp : models)
    temp->Pass(model);
    for (ModelAnimator* temp : animators)
    temp->Pass(anim);
    }

     

     


     

    실행화면

     

     

     

     


     

     

     

     

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