If \( P(x) \) is a polynomial of degree 5 and
\[
\alpha = \sum_{i=0}^{6} P(x_i) \left( \prod_{\substack{j=0
j\neq i}}^{6} (x_i - x_j)^{-1} \right),
\]
where \( x_0, x_1, \ldots, x_6 \) are distinct points in the interval \([2,3]\), then the value of \( \alpha^2 - \alpha + 1 \) is __________.