rand_normal01() = rand(Normal(0, 1))

function update_verlet_list!(args)
    @simd for pv in args.verlet_list
        reset!(pv)
    end

    for i in 1:(args.N - 1)
        for j in (i + 1):(args.N)
            p1 = args.particles[i]
            p2 = args.particles[j]

            overlapping = are_overlapping(p1, p2, args.skin_r², args.l).overlapping

            if overlapping
                push!(args.verlet_list[i], j)
            end
        end
    end

    return nothing
end

function euler!(args)
    for i in 1:(args.N - 1)
        p = args.particles[i]
        verlet_list = args.verlet_list[p.id]

        for j in 1:(verlet_list.last_ind)
            p2 = args.particles[verlet_list.v[j]]

            overlapping, r⃗₁₂, distance² = are_overlapping(
                p, p2, args.interaction_r², args.l
            )

            if overlapping
                c = args.c₁ / (distance²^4) * (args.c₂ / (distance²^3) - 1)

                @simd for k in 1:2
                    dck = c * r⃗₁₂[k]

                    p.tmp_c[k] -= dck
                    p2.tmp_c[k] += dck
                end
            end
        end
    end

    @simd for p in args.particles
        e = SVector(cos(p.φ), sin(p.φ))

        @simd for i in 1:2
            p.tmp_c[i] += args.vδt * e[i] + args.c₃ * rand_normal01()
        end

        p.φ += args.c₄ * rand_normal01()

        restrict_coordinates!(p; l=args.l)

        update!(p)
    end

    return nothing
end

function simulate(
    args,
    δt::Float64,
    T::Float64,
    n_steps_before_verlet_list_update::Int64,
    n_steps_before_save::Int64,
)
    sol = Solution(args.N, args.n_frames)

    frame = 0

    frame = save_frame!(sol, frame, 0.0, args.particles)

    start_time = now()
    println("Started simulation at $start_time.")

    @showprogress 0.6 for (integration_step, t) in enumerate(0:δt:T)
        if integration_step % n_steps_before_save == 0
            frame = save_frame!(sol, frame, t, args.particles)
        end

        if integration_step % n_steps_before_verlet_list_update == 0
            update_verlet_list!(args)
        end

        euler!(args)
    end

    end_time = now()
    elapsed_time = canonicalize(CompoundPeriod(end_time - start_time))
    println("Simulation done at $end_time and took $elapsed_time.")

    return (; sol, end_time)
end