9. Given positive numbers $a, b, c, d$ satisfying $a+b+c+d=1$, find the minimum value of $M=\sqrt{a^{2}+\frac{1}{8 a}}+\sqrt{b^{2}+\frac{1}{8 b}}+\sqrt{c^{2}+\frac{1}{8 c}}+\sqrt{d^{2}+\frac{1}{8 d}}$.