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Bob and Alice play a sport. Bob sends a sequence of optimistic numbers to Alice and utilizing that info she varieties a directed graph.

  • For every quantity within the sequence, she splits it into two non-empty components with none main zeroes and provides a directed edge from the vertex within the left half to the one in the precise. For instance, if she will get the integer $12034$, she will be able to add an edge from vertex $1$ to vertex $2034$ or from vertex $120$ to vertex $34$ or from vertex $1203$ to vertex $4$.
    (12|034 isn’t a legitimate cut up as a result of the precise half accommodates a number one zero)

  • Alice splits every quantity in such a means that the resultant graph after including all the sides has no cycles.

Before beginning the sport, Bob lets Alice know that there’s an edge from vertex $1$ to vertex $1010$.

Can Bob discover a technique to ship a sequence such that Alice at all times finally ends up with a graph containing an edge from vertex $1$ to vertex $21$?

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