CN-TST 2023 Problem 21

Given integer $n\geq 2$ . Find the minimum value of $\lambda {}$ , satisfy that for any real numbers $a_1$ , $a_2$ , $\cdots$ , ${a_n}$ and ${b}$ , $$\lambda\sum\limits_{i=1}^n\sqrt{|a_i-b|}+\sqrt{n\left|\sum\limits_{i=1}^na_i\right|}\geqslant\sum\limits_{i=1}^n\sqrt{|a_i|}.$$