using Base
using DataStructures

found = Dict{Int, Array{Int64}}()

function count_nz(seq)
    return length([i for i in seq if i > 0])
end

for i1 in 0:32
    for i2 in i1:32
        for i3 in i2:32
            for i4 in i3:32
                s = i1 ^ 2 + i2 ^ 2 + i3 ^ 2 + i4 ^ 2

                if s <= 1000
                    seq = [ i1, i2, i3, i4 ]
                    
                    # if !haskey(found, s)
                    #     found[s] = seq
                    # end

                    if haskey(found, s)
                        s_prev = found[s]
                    
                        if count_nz(seq) < count_nz(s_prev)
                            found[s] = seq
                        end
                    else
                        found[s] = seq
                    end
                end
            end 
        end 
    end
end

found = sort(found)

delete!(found, 0)

# for i = 1:1000
#     if haskey(found, i)
#         print("x")
#     else
#         print("_")
#     end 
# end

for (sum, seq) in found
    println("$(join(["$(i)^2" for i in seq if i > 0], " + ")) = $(sum)")
end

# println(length([k for (k, v) in found if length([i for i in v if i != 0]) == 4]))