You are given an array $$$a$$$ consisting of $$$n$$$ integers. You can make any number of partitions in the array such that when you combine all these partitions, the value of the special sum that is obtained is maximum. If you make $$$k$$$ partitions in the array, the the special sum is defined as $$$P_{1} - P_{2} + P_{3} + .... + (-1)^{k+1}P_{k}$$$. Here $$$P_{i}$$$ is defined as the summation of all integers in that partition.