Maximizing a particular sum over all possible subarrays

Consider an array like this one below:

  {1, 5, 3, 5, 4, 1}

When we choose a subarray, we reduce it to the lowest number in the subarray. For example, the subarray {5, 3, 5} becomes {3, 3, 3}. Now, the sum of the subarray is defined as the sum of the resultant subarray. For example, {5, 3, 5} the sum is 3 + 3 + 3 = 9. The task is to find the largest possible sum that can be made from any subarray. For the above array, the largest sum is 12, given by the subarray {5, 3, 5, 4}.

Is it possible to solve this problem in time better than O(n²)?