CF260D Black and White Tree

The board has got a painted tree graph, consisting of $ n $ nodes. Let us remind you that a non-directed graph is called a tree if it is connected and doesn't contain any cycles. Each node of the graph is painted black or white in such a manner that there aren't two nodes of the same color, connected by an edge. Each edge contains its value written on it as a non-negative integer. A bad boy Vasya came up to the board and wrote number $ s_{v} $ near each node $ v $ — the sum of values of all edges that are incident to this node. Then Vasya removed the edges and their values from the board. Your task is to restore the original tree by the node colors and numbers $ s_{v} $ .

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