EGMO 2025 Problem 6

In each cell of a $2025 \times 2025$ 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 $R = r_{1} + r_{2} + \dots + r_{2025}$ . Similarly, define $c_{i}$ to be the largest value in column $i$ , and let $C = c_{1} + c_{2} + \dots + c_{2025}$ .What is the largest possible value of $\frac{R}{C}$ ?

What is the largest possible value of $\frac{R}{C}$ ?