We report large-scale electronic structure calculations for fulminic acid, HCNO, isocyanic acid, HNCO, and cyanic acid, HOCN, in their ground electronic states. The coupled cluster CCSD(T) method including all single and double excitations and a perturbative term for connected triple substitutions is used in conjunction with large correlation consistent polarized valence basis sets of the form cc-pVXZ (X = 2-6) and cc-pCVXZ (X = 2-5). Our results show the importance of including all electrons in the correlation treatment to obtain a converged molecular structure for the extremely floppy HCNO molecule and the correct energetics of the three isomers. All-electron correlation calculations and frozen core calculations with very large basis sets clearly converge towards a linear electronic minimum for HCNO surrounded by a very large flat region of the potential energy surface for hydrogen bending motions. For each of the three isomers we have computed the barrier to linearity along the respective minimum energy path and several spectroscopic parameters and equilibrium rotational constants.