Distances

Arya and Aryan live in a country called Nadaca. Nadaca consists of $N$ cities numbered $1$ through $N$, which are connected by some bidirectional roads. Each road has a positive (not necessarily integer) length. Arya lives in city $1$ and Aryan lives in city $N$. Arya claims that for each city $v$, the shortest path from city $1$ to city $v$ has length $a_v$. Aryan does not disagree, but claims t