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We present the chemical composition of 206 red giant branch stars members of the Small Magellanic Cloud (SMC) using optical, high-resolution spectra collected with the multi-object spectrograph FLAMES-GIRAFFE at the ESO Very Large Telescope. This sample includes stars in three fields located in different positions within the parent galaxy. We analysed the main groups of elements, namely light- (Na), alpha- (O, Mg, Si, Ca, Ti), iron-peak (Sc, V, Fe, Ni, Cu) and s-process elements (Zr, Ba, La). The metallicity distribution of the sample displays a main peak around [Fe/H] ~ -1 dex and a weak metal-poor tail. However, the three fields display [Fe/H] distributions different with each other, in particular a difference of 0.2 dex is found between the mean metallicities of the two most internal fields.The fraction of metal-poor stars increases significantly (from ~1 to ~20%) from the innermost fields to the most external one, likely reflecting an age gradient in the SMC. Also, we found a hint of possible chemically/kinematic distinct substructures. The SMC stars have abundance ratios clearly distinct with respect to the Milky Way stars, in particular for the elements produced by massive stars (like Na, $\alpha$ and most iron-peak elements) that have abundance ratios systematically lower than those measured in our Galaxy. This points out that the massive stars contributed less to the chemical enrichment of the SMC with respect to the Milky Way, according to the low star formation rate expected for this galaxy. Finally, we identified small systematic differences in the abundances of some elements (Na, Ti, V and Zr) in the two innermost fields, suggesting that the chemical enrichment history in the SMC has been not uniform., Comment: 16 pages, 11 figures, 5 tables. Accepted for publication in Astronomy and Astrophysics