Let $(R,\mathfrak m)$ be a Noetherian local ring.

**Definition**: $I$ is called *locally complete intersection* ideal if $I_p$ is a complete intersection for all $p\in V(I)$.

**I want an example of an ideal $I$ satisfying the following three properties:**

1) grade$(I)\geq 1$,

2) $I$ locally complete intersection ideal but not an $\mathfrak m$-primary and complete intersection ideal,

3) $I$ is not integrally closed.

Any suggestion or reference will be extremely helpful. Thank you in advance.