Let \( ABC\) be a triangle, with \( AB=11\) and \( AC=7\), and let \( I, B_1, C_1\) respectively be the incenter, the intersection between the side \( AC\) and the internal bisector \( BI\) of \( \angle ABC\) and the intersection between the side \( AB\) and the internal bisector \( CI\) of \( \angle ACB\). Knowing that \( AB_1C_1I \) are concyclic, and that \(BC=\sqrt{n}\), find \(n\).

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