switch the color of ' grandparent ( in this exampleignore the message that the root must be black switch the color of ' parent ( rotate with ' grandparent ( at the topin the direction that raises (here right rotationg change color rotate change color figure color flip changes and new node inserted outside grandchild on the way down suddenlythe tree is balancedit has also become pleasantly symmetrical this appears to be bit of miraclebut it' only the result of following the color rules now the node with value can be inserted in the usual way because the node it connects to is blackthere' no complexity about the insertion one color flip (at is necessary figure shows the tree after is inserted inside grandchild if is an inside grandchild when red-red conflict occurs on the way downtwo rotations are required to set it right this situation is similar to the inside grandchild in the post-insertion phasewhich we called possibility