Intrinsic photon index Γ_int as a function of the redshift assuming the EBL model from Franceschini et al. (2008). The blue and gray filled areas correspond to the 1σ (68%) and 2σ (95%) confidence error belts, respectively. The red arrow indicates the estimated redshift z^∗, which is determined by the redshift value at which Γ_int = Γ_LAT = 1.83 ± 0.18. The diagonal shaded area shows the error range of z^∗, where the error takes both the errors on the MAGIC VHE photon index and the Fermi-LAT HE photon index into account. See text for calculation of the reconstructed redshift z_rec using the value z^∗. The blue arrow indicates the 95% confidence level upper limit on the redshift, which is obtained when Γ_int = 1.5, within the 2σ (95%) confidence error belt.