Does exponent matter?

Algebra Level pending

Let \((x_i, y_i)\) be ordered pair of solutions of the equation \[x^y + y^x = x + y\] such that \(x_i \leq y_i; x_i, y_i \in \mathbb{Z}; x_i, y_i \in [0, 1000]\) Evaluate \[\sum_{}^{} x_i + y_i\]

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