using JuMP, Gurobi

const GRB_ENV = Gurobi.Env();

nCan = 250 #Number of Candidates
nVotes = 5000 #Number of Votes

m = JuMP.Model(with_optimizer(Gurobi.Optimizer, GRB_ENV, OutputFlag=0))

@variables(m, begin
    0 ≤ y[1:(nVotes+1)] ≤ nCan, Int #Number of candidates at a vote count
    z̄ ≥ 0 #Max number of Candidates
end)

@constraints(m, begin
    totCanCount, sum(y) == nCan
    totVoteCount, y'*collect(0:nVotes) == nVotes
    maxZ, z̄ .≥ y
end)

@objective(m, Min, z̄)
JuMP.optimize!(m)
println(JuMP.termination_status(m))
println(JuMP.value(z̄))