Score : 500 points
For two sequences S and T of length N consisting of 0 and 1, let us define f(S, T) as follows:
Consider repeating the following operation on S so that S will be equal to T. f(S, T) is the minimum possible total cost of those operations.
There are 2^N \times (2^N - 1) pairs (S, T) of different sequences of length N consisting of 0 and 1. Compute the sum of f(S, T) over all of those pairs, modulo (10^9+7).
Input is given from Standard Input in the following format:
N C_1 C_2 \cdots C_N
Print the sum of f(S, T), modulo (10^9+7).
1 1000000000
999999993
There are two pairs (S, T) of different sequences of length 2 consisting of 0 and 1, as follows:
The sum of these is 2000000000, and we should print it modulo (10^9+7), that is, 999999993.
2 5 8
124
There are 12 pairs (S, T) of different sequences of length 3 consisting of 0 and 1, which include:
In this case, if we first change S_1 to 1 then change S_2 to 0, the total cost is 5 \times 2 + 8 = 18. We cannot have S = T at a smaller cost, so f(S, T) = 18.
5 52 67 72 25 79
269312