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
 */

`default_nettype none


module tt_um_multiplier (
    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 array_mult_structural(
    input [3:0] m,
    input [3:0] q,
    output [7:0] p
    );

    wire [3:0] x0_in, x1_in, x2_in, x3_in;
    wire [3:0] int1, int2, int3, int4, int5, int6, int7, int8, int9, int10;

    and(x0_in[0], m[0], q[0]);
    and(x0_in[1], m[0], q[1]);
    and(x0_in[2], m[0], q[2]);
    and(x0_in[3], m[0], q[3]);
    black_box bb_00(x0_in[0], 1'b0, 1'b0, int1[0], int2[0]);
    black_box bb_01(x0_in[1], 1'b0, 1'b0, int1[1], int2[1]);
    black_box bb_02(x0_in[2], 1'b0, 1'b0, int1[2], int2[2]);
    black_box bb_03(x0_in[3], 1'b0, 1'b0, int1[3], int2[3]);

    and(x1_in[0], m[1], q[0]);
    and(x1_in[1], m[1], q[1]);
    and(x1_in[2], m[1], q[2]);
    and(x1_in[3], m[1], q[3]);
    black_box bb_10(x1_in[0], int1[1], int2[0], int3[0], int4[0]);
    black_box bb_11(x1_in[1], int1[2], int2[1], int3[1], int4[1]);
    black_box bb_12(x1_in[2], int1[3], int2[2], int3[2], int4[2]);
    black_box bb_13(x1_in[3], 1'b0, int2[3], int3[3], int4[3]);

    and(x2_in[0], m[2], q[0]);
    and(x2_in[1], m[2], q[1]);
    and(x2_in[2], m[2], q[2]);
    and(x2_in[3], m[2], q[3]);
    black_box bb_20(x2_in[0], int3[1], int4[0], int5[0], int6[0]);
    black_box bb_21(x2_in[1], int3[2], int4[1], int5[1], int6[1]);
    black_box bb_22(x2_in[2], int3[3], int4[2], int5[2], int6[2]);
    black_box bb_23(x2_in[3], 1'b0, int4[3], int5[3], int6[3]);

    and(x3_in[0], m[3], q[0]);
    and(x3_in[1], m[3], q[1]);
    and(x3_in[2], m[3], q[2]);
    and(x3_in[3], m[3], q[3]);
    black_box bb_30(x3_in[0], int5[1], int6[0], int7[0], int8[0]);
    black_box bb_31(x3_in[1], int5[2], int6[1], int7[1], int8[1]);
    black_box bb_32(x3_in[2], int5[3], int6[2], int7[2], int8[2]);
    black_box bb_33(x3_in[3], 1'b0, int6[3], int7[3], int8[3]);

    black_box bb4(int7[1], int8[0], 1'b0, int9[0], int10[0]);
    black_box bb5(int7[2], int8[1], int10[0], int9[1], int10[1]);
    black_box bb6(int7[3], int8[2], int10[1], int9[2], int10[2]);
    black_box bb7(1'b0, int8[3], int10[2], int9[3], int10[3]);

    assign p = {int9[3], int9[2], int9[1], int9[0], int7[0], int5[0], int3[0], int1[0]};

endmodule

module black_box(
    input a,
    input b,
    input c,
    output y,
    output z
    );

// Internal Signals
    wire int_sig1;
    wire int_sig2;
    wire int_sig3;
    wire int_sig4;
    wire int_sig5;
    wire int_sig6;
    wire int_sig7;
    wire int_sig8;

    assign int_sig1 = a & ~b;
    assign int_sig2 = ~a & b;
    assign int_sig3 = int_sig1 + int_sig2;
    assign int_sig4 = int_sig3 & ~c;
    assign int_sig5 = ~int_sig3 & c;
    assign y = int_sig4 + int_sig5;
    assign int_sig6 = a & b;
    assign int_sig7 = b & c;
    assign int_sig8 = c & a;
    assign z = int_sig6 | int_sig7 | int_sig8;

endmodule


Reference solution:
rtl/generated.v: 
  // All output pins must be assigned. If not used, assign to 0.
  array_mult_structural sol(ui_in[7:4], ui_in[3:0], uo_out[7:0]);  // Example: ou_out is the sum of ui_in and uio_in
  assign uio_out = 0;
  assign uio_oe  = 0;

  // List all unused inputs to prevent warnings
  wire _unused = &{ena, clk, rst_n, 1'b0};