Compute
\[\cos^2 0^\circ + \cos^2 1^\circ + \cos^2 2^\circ + \dots + \cos^2 90^\circ.\]The answer is in the form rac{m}{n}, where gcd(m, n) = 1. Please provide the value of m + n.

Let's think step by step and output the final answer within \boxed{}.
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