Use a prefix XOR array to track the cumulative parity of vowels up to each index, where each bit represents the parity (0 for even, 1 for odd) of a vowel's count.

For each index, compute the current mask by XOR-ing the prefix mask with the bit corresponding to the current vowel (if any). If this mask has been seen before, the substring between the first occurrence and the current index has all vowels with even counts.

To handle the case where the substring starts from the beginning, initialize the hash map with `{0: -1}` to represent the empty prefix before the string starts.