Consider an array, , of integers. We define the following terms:

• Subsequence
  A subsequence of is an array that's derived by removing zero or more elements from without changing the order of the remaining elements. Note that a subsequence may have zero elements, and this is called the empty subsequence.

• Strictly Increasing Subsequence
  A non-empty subsequence is strictly increasing if every element of the subsequence is larger than the previous element.

• Subarray
  A subarray of is an array consisting of a contiguous block of 's elements in the inclusive range from index to index . Any subarray of can be denoted by .

The diagram below shows all possible subsequences and subarrays of :

We define the following functions:

• = the maximum sum of some strictly increasing subsequence in subarray

We define the goodness, , of array to be:

In other words, is the maximum possible value of for all possible subarrays of array .

Let be the length of the smallest subarray such that . Given , find the value of as well as the number of subarrays such that and , then print these respective answers as space-separated integers on a single line.