Problem 6 In each cell of a 2025 × 2025 board, a nonnegative real number is written in such a way that the sum of the numbers in each row is equal to 1, and the sum of the numbers in each column is equal to 1. Define r_i to be the largest value in row i, and let R = r₁ + r₂ + · · · + r₂₀₂₅. Similarly, define ci to be the largest value in column i, and let C = c₁ + c₂ + · · · + c₂₀₂₅. What is the largest possible value of  $\frac{R}{C}$ ?