Help with algorithm: calculate max possible score of DigitParty game

General Usage
5

I’ve made an attempt. I believe it correctly establishes all of the constraints. However, I’m struggling with the @objective.

using StaticArrays
using JuMP
using HiGHS

# How the game is defined
mutable struct Game
    board   :: MMatrix{5,5,Int8}
    up_next :: MVector{2,Int8}
end


function get_max_score(g::Game)
    game_is_over(g) || error("Cannot get max score before game is over")

    # Create an array that acts like a dictionary. The index is the number and the value
    # is how many times that number appeared on the board
    counts = @MVector zeros(Int, 9)
    for val in g.board
        counts[val] += 1
    end

    model = Model(HiGHS.Optimizer)
    # Create a 7x7 matrix, where the outer rows and columns are all zeros. Makes getting
    # neighbors easier
    @variable(model, x[1:7, 1:7], Int)

    # All boundaries have to be 0
    @constraint(model, bz1, x[:, 1] .== 0)
    @constraint(model, bz2, x[:, end] .== 0)
    @constraint(model, bz3, x[1, :] .== 0)
    @constraint(model, bz4, x[end, :] .== 0)

    # Need the correct number of instances of each number
    @constraints(
        model,
        begin
            correct_numbers[i = eachindex(counts)], count(==(i), x[2:6, 2:6]) == counts[i]
        end
    )

    # Hoping to use 
    # when `x[idx+dir] >= 1`, we add `x[idx]`, otherwise add 0
    # DIRS = CartesianIndex.([(1, 1), (1, 0), (1, -1), (0, 1), (0, -1), (-1, 1), (-1, 0), (-1, -1)])
    @objective(
        model,
        Max,
        sum(
            x[idx] * (1 - min(x[idx+dir], 1)) for
            idx in eachindex(IndexCartesian(), x[2:6, 2:6]) for dir in DIRS
        )
    )

    optimize!(model)
    @show termination_status(model)
    @show x
end

Any thoughts on how to write the objective?