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 FavoritoHJS
 * SPDX-License-Identifier: Apache-2.0
 */

`default_nettype none

/*IDEA: Parallax scrolling city, 4 layers*/
module tt_um_favoritohjs_scroller (
	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



/*Module parameters are broken, so i have to do this and hope it gets optimized away.*/
module vertical_scheudler(
	input wire clk,
	input wire rst_n,
	input wire hsync,
	input wire vsync,
	input wire [9:0] xpos,
	input wire [9:0] ypos,
	input wire [4:0] LOOP_LENGTH,
	input wire [9:0] START_HEIGHT,
	output wire [4:0] val,
	output wire border
);
	reg started;
	reg [4:0] blockline;
	reg [4:0] blockval;
	reg borderreg;
	assign val = blockval;
	assign border = borderreg;
	always @(posedge clk) begin
		if (~rst_n || ~vsync) begin
			started <= 1'b0;
			blockline <= (LOOP_LENGTH - 1);
			blockval <= 5'b0;
			borderreg <= 1'b0;
		end else begin
			if (ypos == START_HEIGHT) begin
				started <= 1'b1;
			end
			if (started) begin
				if (xpos == 10'd656) begin
					if (blockline == 0) begin
						blockline <= (LOOP_LENGTH - 1);
						if (blockval != 16) begin
							blockval <= blockval + 1;
						end
					end else begin
						blockline <= blockline - 1;
					end
					if (blockline == LOOP_LENGTH - 1) borderreg <= 0;
					if (blockline == 1) borderreg <= 1;
					if (blockline == 0) borderreg <= 1;
				end
			end
		end
	end
endmodule

module color_ditherer(
	input wire clk,
	input wire rst_n,
	input wire dither,
	input wire[2:0] rin,
	input wire[2:0] gin,
	input wire[2:0] bin,
	output wire[1:0] r,
	output wire[1:0] g,
	output wire[1:0] b
);
	reg[1:0] rout;
	reg[1:0] gout;
	reg[1:0] bout;
	assign r = rout;
	assign g = gout;
	assign b = bout;
	always @(posedge clk) begin
		if (~rst_n) begin
			rout <= 0;
			gout <= 0;
			bout <= 0;
		end else begin
			if (dither && rin[0]) rout <= rin[2:1] + 1;
			else rout <= rin[2:1];
			if (dither && gin[0]) gout <= gin[2:1] + 1;
			else gout <= gin[2:1];
			if (dither && bin[0]) bout <= bin[2:1] + 1;
			else bout <= bin[2:1];
		end
	end
endmodule

//https://github.com/algofoogle/tt05-vga-spi-rom/blob/main/src/vga_sync.v
/*TODO: Optimize by doing LFSR shenanigans?*/
module vga_sync(
	input wire clk,
	input wire rst_n,
	output wire[9:0] hcount,
	output wire[9:0] vcount,
	output wire visible,
	output wire vsync,
	output wire hsync
);
	reg[9:0] vga_xpos;
	reg[9:0] vga_ypos;
	reg      vga_vsync, vga_hsync;
	assign vsync = vga_vsync;
	assign hsync = vga_hsync;
	assign hcount = vga_xpos;
	assign vcount = vga_ypos;
	always @(posedge clk) begin
		if (~rst_n) begin
			vga_xpos <= 10'd1;
			vga_ypos <= 10'd1;
		end else begin
			//This code seems very odd, but apparently it works in real hardware?
			//TODO: This can be optimized by only reading the top few bits.
			if (vga_xpos == 10'd800) begin
				vga_xpos <= 1;
				if (vga_ypos == 10'd525) vga_ypos <= 1;
				else vga_ypos <= vga_ypos + 1;
			end
			else vga_xpos <= vga_xpos + 1;
		end

	end

	reg xvisible, yvisible;
	//assign xvisible = (vga_xpos < 10'd641);
	//assign yvisible = (vga_ypos < 10'd481);
	assign visible = xvisible && yvisible;
	always @(posedge clk) begin
		if (~rst_n) begin
			xvisible <= 1'b0;
			yvisible <= 1'b0;
			vga_hsync <= 1'b1;
			vga_vsync <= 1'b1;
		end else begin
			if      (vga_xpos == 10'd1)   xvisible <= 1'b1;
			else if (vga_xpos == 10'd641) xvisible <= 1'b0;
			if      (vga_ypos == 10'd1)   yvisible <= 1'b1;
			else if (vga_ypos == 10'd481) yvisible <= 1'b0;
			if      (vga_xpos == 10'd656) vga_hsync <= 1'b0;
			else if (vga_xpos == 10'd752) vga_hsync <= 1'b1;
			if      (vga_ypos == 10'd490) vga_vsync <= 1'b0;
			else if (vga_ypos == 10'd492) vga_vsync <= 1'b1;
		end
	end
endmodule


Reference solution:
rtl/generated.v: 
	// All output pins must be assigned. If not used, assign to 0.
	// assign uo_out  = ui_in + uio_in;  // Example: ou_out is the sum of ui_in and uio_in
	assign uio_out = 0;
	assign uio_oe  = 0;
	reg[9:0] lfsr1;
	reg[9:0] lfsr1b;
	reg[2:0] count1;
	reg[2:0] count1b;
	wire     hborder1 = (count1 == 0) || (count1 == 1);
	wire     border1 = vborder1 || hborder1;
	reg[9:0] lfsr2;
	reg[9:0] lfsr2b;
	reg[1:0] count2;
	reg[1:0] count2b;
	reg      count2low;
	wire     hborder2 = (count2 == 0) || (count2 == 1);
	wire     border2 = vborder2 || hborder2;
	reg      dither;
	wire     visible;

	wire[4:0] cutoff1;
	wire      vborder1;
	wire[4:0] cutoff2;
	wire      vborder2;

	wire[3:0] l1 = lfsr1[3:0];
	wire[3:0] l2 = lfsr2[3:0];
	//https://github.com/algofoogle/tt05-vga-spi-rom/blob/main/src/test/tb.v
	reg[2:0]  rd,gd,bd;
	wire[1:0]  r, g, b;
	wire      hsync;
	wire      vsync;
	wire[9:0] hcount;
	wire[9:0] vcount;
	assign uo_out[7] = hsync;
	assign uo_out[3] = vsync;
	assign {uo_out[0], uo_out[4]} = r;
	assign {uo_out[1], uo_out[5]} = g;
	assign {uo_out[2], uo_out[6]} = b;


	vga_sync vga_sync(
		.hcount(hcount),
		.vcount(vcount),
		.hsync(hsync),
		.vsync(vsync),
		.visible(visible),
		.clk(clk),
		.rst_n(rst_n)
	);
	color_ditherer color_ditherer(
		.clk(clk),
		.rst_n(rst_n),
		.dither(dither),
		.rin(rd),
		.gin(gd),
		.bin(bd),
		.r(r),
		.g(g),
		.b(b)
	);
	/*Module parameters are broken, so i have to do this and hope it gets optimized away.*/
	vertical_scheudler vscheudler1 (
		.clk(clk),
		.rst_n(rst_n),
		.hsync(hsync),
		.vsync(vsync),
		.xpos(hcount),
		.ypos(vcount),
		.START_HEIGHT(10'd116),
		.LOOP_LENGTH(5'd16),
		.val(cutoff1),
		.border(vborder1));

	vertical_scheudler vscheudler2 (
		.clk(clk),
		.rst_n(rst_n),
		.hsync(hsync),
		.vsync(vsync),
		.xpos(hcount),
		.ypos(vcount),
		.START_HEIGHT(10'd184),
		.LOOP_LENGTH(5'd8),
		.val(cutoff2),
		.border(vborder2));

	//https://stackoverflow.com/questions/12504837/verilog-generate-genvar-in-an-always-block
	/*
	genvar i;
	generate
		for (i=0; i<=16; i=i+1) begin
			always @(posedge clk) begin
				if (rst_n) begin
					if (vcount == 112 + (i*16)) cutoff1 <= i;
					if (vcount == 112 + (i*16)) vborder1 <= 1;
					if (vcount == 112 + (i*16) + 1) vborder1 <= 0;
					if (vcount == 112 + (i*16) + 15) vborder1 <= 1;
					if (vcount == 176 + (i*8)) cutoff2 <= i;
				end
			end
		end
	endgenerate
	*/
	always @(posedge clk) begin
		if (~rst_n) begin
			lfsr1 <= 10'h3ff;
			lfsr1b <= 10'h3ff;
			count1 <= 3'd7;
			count1b <= 3'd7;
			lfsr2 <= 10'h10f;
			lfsr2b <= 10'h10f;
			count2 <= 2'd3;
			count2b <= 2'd3;
			count2low <= 1'b1;
			//cutoff2 <= 5'd0;
			dither <= 1'b0;
			rd <= 3'b000;
			gd <= 3'b000;
			bd <= 3'b000;
		end else begin
			// TODO: Read multiple bits out at the same time.
			// https://zipcpu.com/dsp/2017/11/13/lfsr-multi.html
			if (visible) begin
				dither <= ~dither;
				count1 <= count1 + 1;
				if (count1 == 0) begin
					lfsr1[0] <= lfsr1[9] ^ lfsr1[6];
					lfsr1[1] <= lfsr1[8] ^ lfsr1[5];
					lfsr1[2] <= lfsr1[7] ^ lfsr1[4];
					lfsr1[3] <= lfsr1[6] ^ lfsr1[3];
					lfsr1[9:4] <= lfsr1[5:0];
				end
				count2 <= count2 + 1;
				if (count2 == 0) begin
					lfsr2[0] <= lfsr2[9] ^ lfsr2[6];
					lfsr2[1] <= lfsr2[8] ^ lfsr2[5];
					lfsr2[2] <= lfsr2[7] ^ lfsr2[4];
					lfsr2[3] <= lfsr2[6] ^ lfsr2[3];
					lfsr2[9:4] <= lfsr2[5:0];
				end
			end
			//This is executed once per scanline
			if (hcount == 656) begin
				dither <= ~dither;
				//if (vcount == 1)   cutoff1 <= 0;
				//if (vcount == 1)   cutoff2 <= 0;

				//and this once per frame
				if (vcount == 482) begin
					count1b <= count1b  + 1;
					if (count1b == 0) begin
						lfsr1b[0] <= lfsr1b[9] ^ lfsr1b[6];
						lfsr1b[1] <= lfsr1b[8] ^ lfsr1b[5];
						lfsr1b[2] <= lfsr1b[7] ^ lfsr1b[4];
						lfsr1b[3] <= lfsr1b[6] ^ lfsr1b[3];
						lfsr1b[9:4] <= lfsr1b[5:0];
					end
					{count2b, count2low}<= {count2b, count2low} + 3'd1;
					if (count2b == 0 & count2low == 1) begin
						lfsr2b[0] <= lfsr2b[9] ^ lfsr2b[6];
						lfsr2b[1] <= lfsr2b[8] ^ lfsr2b[5];
						lfsr2b[2] <= lfsr2b[7] ^ lfsr2b[4];
						lfsr2b[3] <= lfsr2b[6] ^ lfsr2b[3];
						lfsr2b[9:4] <= lfsr2b[5:0];
					end
				end
				lfsr1 <= lfsr1b;
				lfsr2 <= lfsr2b;
				count1 <= count1b;
				count2 <= count2b;
			end
			//thanks @Ravenslofty and @a1k0n for alerting me of this block and
			//how it needs to be inlined with the main block to prevent
			//conflicting drivers
			if (visible) begin
				if ({1'b0, l1} < cutoff1) begin
					if (border1) begin
						rd <= 3'b011;
						gd <= 3'b011;
						bd <= 3'b110;
					end else begin
						rd <= 3'b110;
						gd <= 3'b110;
						bd <= 3'b101;
					end
				end else if ({1'b0, l2} < cutoff2) begin
					if (border2) begin
						rd <= 3'b010;
						gd <= 3'b010;
						bd <= 3'b100;
					end else begin
						rd <= 3'b100;
						gd <= 3'b100;
						bd <= 3'b101;
					end
				end else begin
					rd <= 3'b010;
					gd <= 3'b010;
					bd <= 3'b011;
				end
			end else begin
				rd <= 3'b000;
				gd <= 3'b000;
				bd <= 3'b000;
			end
		end
	end
	// List all unused inputs to prevent warnings
	wire _unused = &{ena, 1'b0};