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 Your Name
 * SPDX-License-Identifier: Apache-2.0
 */

`define default_netname none

module tt_um_pckys_game (
    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,      // will go high when the design is enabled
    input  wire       clk,      // clock
    input  wire       rst_n     // reset_n - low to reset
);

  // All output pins must be assigned. If not used, assign to 0.
  assign uio_out = 0;
  assign uio_oe  = 0;
  assign DI = ui_in;
  assign uo_out = DO;

  reg [7:0] DI,DO;
  
  reg rst;
  assign rst = !rst_n;
    
  reg [7:0] counter;
  reg [7:0] number;
  reg [11:0] counter2;
  reg [2:0] counter3;

  reg [7:0] pattern0;  
  reg [7:0] pattern1;
  reg [7:0] pattern2;
  reg start = 0;
  
  assign DO = (start)?
    ((rst)?pattern1:
    (DI>number)?8'b01000001:
    (DI==number)?pattern2:
    (DI<number)?8'b01001000:
    0):pattern0;

  
  always @(posedge clk )
  begin
    if (rst) begin
        start <= 1;
        number <= counter;
    end
  end

  number_init n_init_inst (clk, rst, counter);
  timer t_inst (clk, counter2, counter3);

assign pattern0 =  
  (counter3 == 0) ? 8'b11010000 :
  (counter3 == 1) ? 8'b11010000 :
  (counter3 == 2) ? 8'b11010000 :
  (counter3 == 3) ? 8'b01010000 :
  (counter3 == 4) ? 8'b01010000 :
                    8'b01010000 ;

assign pattern1 =  
  (counter3 == 0) ? 8'b10100000 :
  (counter3 == 1) ? 8'b00010000 :
  (counter3 == 2) ? 8'b00001000 :
  (counter3 == 3) ? 8'b10000100 :
  (counter3 == 4) ? 8'b00000010 :
                    8'b00000001 ;

assign pattern2 =  
  (counter3 == 0) ? 8'b01000000 :
  (counter3 == 1) ? 8'b01000000 :
  (counter3 == 2) ? 8'b01000000 :
  (counter3 == 3) ? 8'b01001001 :
  (counter3 == 4) ? 8'b01001001 :
                    8'b01001001 ;
  
endmodule

module number_init(
  input clk,
  input rst,
  output [7:0] out
);
// >>> Module Implementation Begin

// <<< Module Implementation End
endmodule



module timer(input clk, output reg [11:0] counter = 12'h0 + 12'd512, output reg [2:0] counter2 = 0);

    reg flag1 = 0;
    
    always @(posedge clk) begin
        counter <= counter + 1'b1;
      if (counter[9]) begin
        if(counter2 == 6)
                counter2 <= 0;
        if(flag1) begin
          flag1 <= 0;
          if(counter2 == 6)
                counter2 <= 0;
         else
          counter2 <= counter2 + 1;
        end
      end else begin
        flag1 <= 1;
      end
    end
    
endmodule


Reference solution:
rtl/generated.v: 
  reg [7:0] counter;
  assign out = counter;

  always @(posedge clk )
  begin
    counter <= 0;
    if (rst) begin
        counter <= counter + 1;
    end else begin
    end
  end