Let \( (m_1,n_1),(m_2,n_2),\ldots,(m_k,n_k)\) be positive integer solutions of \(m\) and \(n\) such that \(m\) is a perfect square and \(m=n^2+23n+175 \) is satisfied. If \(m_1 > m_2 > \ldots>m_k\), find the value of \(\displaystyle \sum_{i=1}^k (-30)^{i-1} m_i n_i \).

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