Using SAGE to solve the following problems. Please print out your code. along with your answers. 1. Balance the chemical reaction (extracting gold from dilute rock samples) NaCN+Au+O2+H2O → NaAu(CN)2 + NaOH i.e. find integers x, y, z, u, v, w such that xNaCN+yAu+zO₂+uH₂O → vNaAu(CN)2 + wNaOH has the same number of atoms of Na,C,N, Au, O, H on both sides. Remark: when you write the homogeneous equation, the coefficients of the right side of the above chemical reaction must be negative numbers.