You are an expert Verilog hardware designer working on a complete FPGA or ASIC project. You are given the full source code of a Verilog project. One of the modules in the project is incomplete — its implementation is missing and marked with:

// >>> Module Implementation Begin

// <<< Module Implementation End

Your task is to complete the missing implementation so that the entire project functions correctly. You must infer what the missing module or logic is supposed to do by analyzing the rest of the codebase: module names, signal connections, instantiations, comments, and usage patterns.

Follow these rules:

1. Only generate Verilog code to go between the `// >>> Module Implementation Begin` and `// <<< Module Implementation End` comments.
2. Use Verilog-2001 syntax. Ensure the code is synthesizable.
3. Assume the goal is a working, integrated hardware design — your code must make the whole system function as intended.
4. Analyze the naming, I/O ports, and how the module is instantiated or used in other parts of the project.
5. Implement correct behavior based on design context. Do not guess randomly — reason it out.
6. Avoid vendor-specific features unless explicitly required.
7. Do not output comments, explanation, or anything outside the required code region unless explicitly asked.

Your output should contain **only the Verilog code** that fits inside the marked region.

/*
 * Copyright (c) 2024 Barak Hoffer
 * SPDX-License-Identifier: Apache-2.0
 */

`default_nettype none

module tt_um_vga_snake (
    input  wire [7:0] ui_in,    // Dedicated inputs
    output wire [7:0] uo_out,   // Dedicated outputs
    input  wire [7:0] uio_in,   // IOs: Input path
    output wire [7:0] uio_out,  // IOs: Output path
    output wire [7:0] uio_oe,   // IOs: Enable path (active high: 0=input, 1=output)
    input  wire       ena,      // always 1 when the design is powered, so you can ignore it
    input  wire       clk,      // clock
    input  wire       rst_n     // reset_n - low to reset
);
// >>> Module Implementation Begin

// <<< Module Implementation End
endmodule




`default_nettype none
//////////////////////////////////////////////////////////////////////////////////
// Company: Ridotech
// Engineer: Juan Manuel Rico
// 
// Create Date:    09:34:23 30/09/2017 
// Module Name:    vga_controller
// Description:    Basic control for 640x480@72Hz VGA signal.
//
// Dependencies: 
//
// Revision: 
// Revision 0.01 - File Created for Roland Coeurjoly (RCoeurjoly) in 640x480@85Hz.
// Revision 0.02 - Change for 640x480@60Hz.
// Revision 0.03 - Solved some mistakes.
// Revision 0.04 - Change for 640x480@72Hz and output signals 'activevideo'
//                 and 'px_clk'.
//
// Additional Comments: 
//
//////////////////////////////////////////////////////////////////////////////////
module VgaSyncGen (
            input wire       px_clk,        // Input clock: 31.5MHz
            input wire       reset,         // reset
            output wire      hsync,         // Horizontal sync out
            output wire      vsync,         // Vertical sync out
            output reg [9:0] x_px,          // X position for actual pixel.
            output reg [9:0] y_px,          // Y position for actual pixel.
            output wire      activevideo
         );

    /*
    http://www.epanorama.net/faq/vga2rgb/calc.html
    [*User-Defined_mode,(640X480)]
    PIXEL_CLK   =   31500
    H_DISP      =   640
    V_DISP      =   480
    H_FPORCH    =   24
    H_SYNC      =   40
    H_BPORCH    =   128
    V_FPORCH    =   9
    V_SYNC      =   3
    V_BPORCH    =   28
    */

    // Video structure constants.
    parameter activeHvideo = 640;               // Width of visible pixels.
    parameter activeVvideo =  480;              // Height of visible lines.
    parameter hfp = 24;                         // Horizontal front porch length.
    parameter hpulse = 40;                      // Hsync pulse length.
    parameter hbp = 128;                        // Horizontal back porch length.
    parameter vfp = 9;                          // Vertical front porch length.
    parameter vpulse = 3;                       // Vsync pulse length.
    parameter vbp = 28;                         // Vertical back porch length.
    parameter blackH = hfp + hpulse + hbp;      // Hide pixels in one line.
    parameter blackV = vfp + vpulse + vbp;      // Hide lines in one frame.
    parameter hpixels = blackH + activeHvideo;  // Total horizontal pixels.
    parameter vlines = blackV + activeVvideo;   // Total lines.

    // Registers for storing the horizontal & vertical counters.
    reg [9:0] hc;
    reg [9:0] vc;

    // Counting pixels.
    always @(posedge px_clk)
    begin
        if(reset) begin
            hc <= 0;
            vc <= 0;
        end else begin
            // Keep counting until the end of the line.
            if (hc < hpixels - 1)
                hc <= hc + 1;
            else
            // When we hit the end of the line, reset the horizontal
            // counter and increment the vertical counter.
            // If vertical counter is at the end of the frame, then
            // reset that one too.
            begin
                hc <= 0;
                if (vc < vlines - 1)
                vc <= vc + 1;
            else
               vc <= 0;
            end
        end
     end

    // Generate sync pulses (active low) and active video.
    assign hsync = (hc >= hfp && hc < hfp + hpulse) ? 0:1;
    assign vsync = (vc >= vfp && vc < vfp + vpulse) ? 0:1;
    assign activevideo = (hc >= blackH && vc >= blackV) ? 1:0;

    // Generate color.
    always @(posedge px_clk)
    begin
        if(reset) begin
            x_px <= 0;
            y_px <= 0;
        end else begin
            x_px <= hc - blackH;
            y_px <= vc - blackV;
        end
     end
 endmodule
`default_nettype wire


module snake(clk, rst_n, x_px, y_px, rrggbb, left, right, up, down);
    input clk;
    input rst_n;
    input [9:0] x_px;
    input [9:0] y_px;
    input left;
    input right;
    input up;
    input down;
    output wire [5:0] rrggbb;

    localparam MAX_SIZE = 6;

    reg [MAX_SIZE*10-1:0] snakeX = {(MAX_SIZE){10'd100}}, snakeY={(MAX_SIZE){10'd100}};
    reg [9:0] appleX = 10'd150, appleY = 10'd150;
    reg [9:0] prev_y;
    reg [2:0] size = 3'd0;
    reg [9:0] appleX_n, appleY_n;
    reg [1:0] direction = 2'b01;
    reg eat_apple;
    reg game_over;
    
    wire [MAX_SIZE-1:0] body;
    wire [MAX_SIZE-1:0] bodySize;
    wire clk;
    wire border, apple;
    wire R, G, B;
    
    assign R = game_over | apple;
    assign bodySize = body[MAX_SIZE-1:0] & ({(MAX_SIZE){1'b1}} >> (MAX_SIZE-size-1));
    assign G = (|bodySize) && !game_over;
    assign B = border && !game_over;

    assign rrggbb = {R, R, G, G, B, B};
    
    always @(posedge clk) begin
        if (!rst_n) 
            direction <= 2'b01;
        else if (left)
            direction <= 2'b00;
        else if (right)
            direction <= 2'b01;
        else if (up)
            direction <= 2'b10;
        else if (down)
            direction <= 2'b11;
    end

    always @(posedge clk)
    begin
        if(!rst_n)
            game_over <= 1'b0;
        else if((border && bodySize[0]) || (|(bodySize[MAX_SIZE-1:1]) && bodySize[0])) 
            game_over <= 1'b1;
    end

    generate
        genvar i;
        for (i = 0; i < MAX_SIZE; i = i+1) begin
            assign body[i] = ((x_px > snakeX[i*10+9:i*10] && x_px < snakeX[i*10+9:i*10]+10) && 
                                (y_px > snakeY[i*10+9:i*10] && y_px < snakeY[i*10+9:i*10]+10));
        end
    endgenerate

    assign border = (x_px < 11) || (x_px > 629) || (y_px < 11) || (y_px > 469);
    assign apple = ((x_px > appleX && x_px < appleX+10) && 
                 (y_px > appleY && y_px < appleY+10));    
        
    always @*
    begin
        case(direction)
            2'b00: begin
                appleX_n = appleX + 30;
                appleY_n = appleY + 120;
            end
            2'b01: begin
                appleX_n = appleX + 70;
                appleY_n = appleY + 140;
            end
            2'b10: begin
                appleX_n = appleX + 60;
                appleY_n = appleY + 40;
            end
            2'b11: begin
                appleX_n = appleX + 80;
                appleY_n = appleY + 20;
            end                    
        endcase
        if (appleX_n < 11)
            appleX_n = 11;
        if (appleX_n > 619)
            appleX_n = 310;
        if (appleY_n < 11)
            appleY_n = 11;
        if (appleY_n > 459)
            appleY_n = 250;            
    end

    always @(posedge clk)
    begin
        if(!rst_n) begin
            snakeX <= {{(MAX_SIZE-1){10'd700}},10'd100};
            snakeY <= {{(MAX_SIZE-1){10'd700}},10'd100};
            appleX <= 10'd150;
            appleY <= 10'd150;
            size <= 0;
            prev_y  <= 10'b0;
            eat_apple <= 1'b0;
        end
        else
        begin
            prev_y <= y_px;
            if (prev_y != y_px && (y_px == 0)) begin
                case(direction)
                    2'b00: snakeX[9:0] <= snakeX[9:0] - 10;
                    2'b01: snakeX[9:0] <= snakeX[9:0] + 10;
                    2'b10: snakeY[9:0] <= snakeY[9:0] - 10;
                    2'b11: snakeY[9:0] <= snakeY[9:0] + 10;
                endcase
                snakeX[MAX_SIZE*10-1:10] <= snakeX[(MAX_SIZE-1)*10-1:0];
                snakeY[MAX_SIZE*10-1:10] <= snakeY[(MAX_SIZE-1)*10-1:0];

                if(eat_apple) begin
                    if (size < MAX_SIZE-1)
                        size <= size + 1;
                    eat_apple <= 0;
                    appleX <= appleX_n;
                    appleY <= appleY_n;
                end

            end
            else if((apple && bodySize[0]))
                eat_apple <= 1'b1;

        end
    end
    
endmodule



Reference solution:
rtl/generated.v: 
  // All output pins must be assigned. If not used, assign to 0.
  assign uio_out = 0;
  assign uio_oe  = 0;

  assign uio_out = 8'b0;
  assign uio_oe  = 8'b0;

  // List all unused inputs to prevent warnings
  wire _unused = &{ena, uio_in, ui_in[7:4], 1'b0};

  wire [5:0] rrggbb, rrggbb_snake;
  wire [9:0] x_px;  // X position for actual pixel.
  wire [9:0] y_px;  // Y position for actual pixel.
  wire hsync, vsync, activevideo;

  assign uo_out[0] = rrggbb[5]; // R[1]
  assign uo_out[1] = rrggbb[3]; // G[1]
  assign uo_out[2] = rrggbb[1]; // B[1]
  assign uo_out[3] = vsync;
  assign uo_out[4] = rrggbb[4]; // R[0]
  assign uo_out[5] = rrggbb[2]; // G[1]
  assign uo_out[6] = rrggbb[0]; // B[0]
  assign uo_out[7] = hsync;

  assign rrggbb = activevideo ? rrggbb_snake : 6'b0;

  VgaSyncGen vga_0 (
      .px_clk(clk),
      .hsync(hsync),
      .vsync(vsync),
      .x_px(x_px),
      .y_px(y_px),
      .activevideo(activevideo),
      .reset(~rst_n)
  );

  snake u_snake (
        .clk(clk),
        .rst_n(rst_n),
        .x_px(x_px),
        .y_px(y_px),
        .left(ui_in[0]),
        .right(ui_in[1]),
        .up(ui_in[2]),
        .down(ui_in[3]),
        .rrggbb(rrggbb_snake)
  );