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You are given a graph $$G$$ consisting of $$N$$ nodes and $$M$$ edges. Each node of $$G$$ is either colored in black or white. Also, each edge of $$G$$ has a particular wieight. Now, you need to find the least expensive path between node $$1$$ and node $$N$$, such that difference of the number of black nodes and white nodes on the path is no more than $$1$$.
It is guaranteed $$G$$ does not consist of multiple edges and self loops.
Input Format:
The first line contains two space separated integers $$N$$ and $$M$$. Each of the next $$M$$ lines contains $$3$$ space separated integers $$ u,v,l $$ which denotes that there is an edge from node $$u$$ to node $$v$$ having a weight $$l$$. The next line contains $$N$$ space separated integers where each integer is either $$0$$ or $$1$$. If the $$ i^{th}$$ integer is $$0$$ it denotes that $$i^{th}$$ node is black , otherwise it is white.
Constraints
$$ 1 \le N \le 1000 $$
$$ 1 \le M \le 10000 $$
$$ 1 \le l \le 1000 $$
$$ 1 \le u , v \le N, u \ne v $$
Output Format
Output a single integer denoting the length of the optimal path fulfilling the requirements. Print -1 if there is no such path.
The optimal path satisfying all the conditions would be :
$$ 1->2->3->5->6 $$