B"There are n cities and m bidirectional roads in the country. The roads in the country form an undirected weighted graph. The graph is not guaranteed to be connected. Each road has it's own parameter w . You can travel through the roads, but the government made a new law: you can only go through two roads at a time (go from city a to city b and then from city b to city c ) and you will have to pay (w_{ab} + w_{bc})^2 money to go through those roads. Find out whether it is possible to travel from city 1 to every other city t and what's the minimum amount of money you need to get from 1 to t . First line contains two integers n , m ( 2 <= q n <= q 10^5 , 1 <= q m <= q min( frac{n cdot (n - 1)}{2}, 2 cdot 10^5) ). Next m lines each contain three integers v_i , u_i , w_i ( 1 <= q v_i, u_i <= q n , 1 <= q w_i <= q 50 , u_i neq v_i ). It's guaranteed that there are no multiple edges, i.e. for any edge (u_i, v_i) there are no other edges (u_i, v_i) or (v_i, u_i) . For every city t print one integer. If there is no correct path between 1 and t output -1 . Otherwise print out the minimum amount of money needed to travel from 1 to t . The graph in the first example looks like this. In the second example the path from 1 to 3 goes through 2 , so the resulting payment is (1 + 2)^2 = 9 . "...