two player Red Blue time they re play crayon the mischievous duo vandalizing root tree coloring node play favorite gameThe game work follow tree size n root node 1 node initially white Red Blue turn Red go in Reds turn follow operation number time Pick subtree root tree color node subtree red However game fair Red allow color k node tree in word Reds turn k node color redthen Blues turn Blue follow operation number time Pick subtree root tree color node subtree blue however he s allow choose subtree contain node color red node purple like purple crayon note there s restriction number nod blue color long do not color node Red coloredafter turn score game determine follow let w number white node r number red node b number blue node the score game w cdot r bRed want maximize score Blue want minimize if player play optimally final score game