Uryson width of three dimensional mean convex domain with non-negative Ricci curvature

We prove that for every three dimensional manifold with nonnegative Ricci curvature and strictly mean convex boundary (non-empty), there exists a Morse function so each connected component of its level sets has uniform diameter bound, which depends only on the lower bound curvature. This gives an upper Uryson 1-width those manifolds boundary.