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Given a graph having N vertices and M bidirectional edges, with each edge having some length and some destruction cost. You have to increase the length of the shortest path between vertex 1 and vertex N, for that you can destroy some edges. Find the minimum cost of doing it.
Input Format:
First line consists of two space separated integers denoting N and M.
Following M lines consists of four space separated integers \(X \; Y \; D \; C\) denoting that there is an edge between vertex X and Y having length D and destruction cost C.
Output Format:
Print the required answer.
Constraints:
\(2 \le N \le 1000\)
\(1 \le M \le 4 \times 10^5\)
\(1 \le X, Y \le N\)
\(1 \le D, C \le 1000000\)
Currently the shortest path between 1 and 4 is of length 1, so we delete this vertex at a cost of 8, so that the length of shortest path increases to 9.