Calculate distance from a point in $\mathbb{R}^n$ to the norm $\ell_1$ unit ball

Question

Given the ball of center $0$, radius $1$ in norm $\ell_1$

$$B(0,1) := \left\{ x \in \mathbb{R}^n : \Vert x \Vert_1 \le 1 \right\}.$$

calculate the distance $d_B(x)$ from a point $x \in \mathbb{R}^n$ to $B(0,1)$, where $d_B(x)$ defined by

$$d_{B}(x) := \inf\left\{\Vert x-c \Vert_2: c \in B(0,1) \right\}, \quad \forall x \in \mathbb{R}^n.$$

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My attempt

I considered two cases

1. If $x \in B(0,1)$ then $d_B(x)=0$.

2. If $x \notin B(0,1)$. I have tried to use many inequality to find the minimum point of this distance but I still can't find it.