every node in the tree should have the what is its need of brackets. For example you can maintain a variable called balance for which you have the following:

balance = 0 — the interval to which the node corresponds is balanced balance = x (x>0) — the interval needs x closing brackets balance = x (x<0) — the interval needs x opening brackets

You should make the changes in the update function and your query function would simply check if the balance of the root is 0

Update: this balance thing should be implemented by separating the needs for every node this means that you must keep needOpening and needClosing for every node