Comonotone approximation with interpolation at the ends on an interval

Let a function f ∈ C[−1, 1], changes its monotonisity at the finite collection Y:= {y₁, ..., y_s} of s points y_i ∈ (−1, 1). For each n ≥ N(Y), we construct an algebraic polynomial P_n, of degree ≤ n, which is comonotone with f, that is changes its monotonisity at the same points y_i as f, and where N(Y) is a constant depending only on Y, c(s) is a constant depending only on s and ω₂ (f,t) is the second modulus of smoothness of f.