A family tree is a chart representing family relationships, in which each parent is connected to their children. Consider a family tree listing only a person's direct ancestors, i.e., only father, mother, paternal grandfather, paternal grandmother, maternal grandfather, Maternal grandmother, ete, without any siblings, such as the following example: and why great grand grand ort grand whe ge her the grand othes father Grand mothay father more father Son Assume that you can color this tree, giving a different color to each person. Prove by induction that it is possible to color a family tree with n generations in a way that no direct parents have the same color (no parent has the same color as their child, but may have the same color as their grandchild) using at most 2 colors. For example: grand pathy grand wher groot grand Whe great grand Jatha greal grand grethe grand wher great grand othes great grand grand protag grand father grand mothey father mother father son.