Expected Repetitions

You are given a string $S$ with length $N$ that contains only the $26$ lowercase English letters. You are also given a sequence $W_1, W_2, \ldots, W_{26}$ of weights corresponding to these letters in the order from 'a' to 'z', i.e. $W_1$ is the weight of 'a', $W_2$ is the weight of 'b' and so on. We define the *weight* of a string as the sum of weights of all characters present in it. If a char