Recall that in a $2-3-4$ tree, whenever we insert a new key we immediately split $($on our way downthe tree$)$ any node we see that is full $($has $3$ keys in it$).$ In the worst case, every node that we seeis full and has to be split, so the number of splits that we do in a single operation can be $($log n$).$Prove that the amortized number of splits is only O$(1).$