Consider two indices, <code>x</code> on the left side and its symmetrical index <code>y</code> on the right side.

Store the frequencies of all of the letters in both intervals <code>[a_i, b_i]</code> and <code>[c_i, d_i]</code> in a query.

If <code>x</code> is not in <code>[a_i, b_i]</code> and <code>y</code> is not in <code>[c_i, d_i]</code>, they must be the same.

If <code>x</code> is in <code>[a_i, b_i]</code> and <code>y</code> is not in <code>[c_i, d_i]</code>, remove one occurrence of the character at index <code>y</code> from the frequency array on the left side.

Similarly, if <code>x</code> is not in <code>[a_i, b_i]</code> and <code>y</code> is in <code>[c_i, d_i]</code>, remove one occurrence of the character at index <code>x</code> from the frequency array on the right side.

Finally, check whether the two frequency arrays are the same, and the indices that don't fall into any of the intervals are the same as well.

Use prefix-sum + hashing to improve the time complexity.