Serial Blasts

Gotham has $N$ cities numbered $1$ to $N$. Joker has planted a bomb in each city such that the bomb in city $i$ destroys at time $i$. All roads coming in and going out of the city get destroyed with it. You are given a matrix $E$ such that $E_{i, j}$ is a positive integer if there is a road from city $i$ to $j$. It specifies cost of going from city $i$ to city $j$. $E_{i, j}$ is not necessarily e