Let $a, b, c, d$ be in arithmetic progression with common difference $\lambda$. If $\left|\begin{array}{ccc}x-a-c & x+b & x+a \\ x-1 & x+c & x+b \\ x-b+d & x+d & x+c\end{array}\right|=2$, then value of $\lambda^2$ is equal to $\_\_\_\_$ .
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