Let \( \vec{a} = 2\hat{i} - \hat{j} + \hat{k} \) and \( \vec{b} = \lambda \hat{j} + 2\hat{k}, \lambda \in \mathbb{Z} \) be two vectors. Let \( \vec{c} = \vec{a} \times \vec{b} \) and \( \vec{d} \) be a vector of magnitude \( 2 \) in \( yz \)-plane. If \( |\vec{c}| = \sqrt{53} \), then the maximum possible value of \( (\vec{c}\cdot \vec{d})^2 \) is equal to:
