The graph shown below has 8 edges with distinct integer edge weights. The minimum spanning tree (MST) is of weight 36 and contains the edges: {(A, C), (B, C), (B, E), (E, F), (D, F)}. The edge weights of only those edges which are in the MST are given in the figure shown below. The minimum possible sum of weights of all 8 edges of this graph is ___________.

A Young tableau is a $$2D$$ array of integers increasing from left to right and from top to bottom. Any unfilled entries are marked with $$\infty ,$$ and hence there cannot be any entry to the right of, or below a $$\infty .$$ The following Young tableau consists of unique entries.

1	2	5	14
3	4	6	23
10	12	18	25
31	∞	∞	∞

When an element is removed from a Young tableau, other elements should be moved into its place so that the resulting table is still a Young tableau (unfilled entries may be filled in with a $$\infty $$). The minimum number of entries (other than $$1$$) to be shifted, to remove $$1$$ from the given Young tableau is ______________.

Suppose P, Q, R, S, T are sorted sequences having lengths 20, 24, 30, 35, 50 respectively. They are to be merged into a single sequence by merging together two sequences at a time. The number of comparisons that will be needed in the worst case by the optimal algorithm for doing this is ____.

The number of distinct minimum spanning trees for the weighted graph below is ________