Minimum of Degrees

There is a graph with N vertices and no edges. Chef is going to add all N*(N-1)/2 possible undirected edges to the graph, in a random order. The cost of adding an edge between vertices x and y is equal to min(degree(x), degree(y)). Here, degree(x) denotes the number of edges incident on x before adding the new edge (between x and y). Find the expected total cost of adding all the edges and print