Determina todos los números de cuatro dígitos $\bar{a}\bar{b}\bar{c}\bar{d}$ tales que\n$$a(a+b+c+d)(a^{2}+b^{2}+c^{2}+d^{2})(a^{6}+2b^{6}+3c^{6}+4d^{6})=\bar{a}\bar{b}\bar{c}\bar{d}$$\n