<image>Given the 100 natural numbers 1, 2, 3, ..., 100, randomly divide them into 50 groups, each containing two numbers. Denote one number as \textit{a} and the other as \textit{b}, and substitute them into the algebraic expression  for calculation. After substituting 50 pairs, 50 values are obtained. Find the minimum sum of these 50 values (please briefly explain the reason).