# 2281 Sum of Total Strength of Wizards

As the ruler of a kingdom, you have an army of wizards at your command.

You are given a 0-indexed integer array `strength`, where `strength[i]` denotes the strength of the `ith` wizard. For a contiguous group of wizards (i.e. the wizards' strengths form a subarray of `strength`), the total strength is defined as the product of the following two values:

• The strength of the weakest wizard in the group.
• The total of all the individual strengths of the wizards in the group.

Return the sum of the total strengths of all contiguous groups of wizards. Since the answer may be very large, return it modulo `109 + 7`.

A subarray is a contiguous non-empty sequence of elements within an array.

Example 1:

``````Input: strength = [1,3,1,2]
Output: 44
Explanation: The following are all the contiguous groups of wizards:
-  from [1,3,1,2] has a total strength of min() * sum() = 1 * 1 = 1
-  from [1,3,1,2] has a total strength of min() * sum() = 3 * 3 = 9
-  from [1,3,1,2] has a total strength of min() * sum() = 1 * 1 = 1
-  from [1,3,1,2] has a total strength of min() * sum() = 2 * 2 = 4
- [1,3] from [1,3,1,2] has a total strength of min([1,3]) * sum([1,3]) = 1 * 4 = 4
- [3,1] from [1,3,1,2] has a total strength of min([3,1]) * sum([3,1]) = 1 * 4 = 4
- [1,2] from [1,3,1,2] has a total strength of min([1,2]) * sum([1,2]) = 1 * 3 = 3
- [1,3,1] from [1,3,1,2] has a total strength of min([1,3,1]) * sum([1,3,1]) = 1 * 5 = 5
- [3,1,2] from [1,3,1,2] has a total strength of min([3,1,2]) * sum([3,1,2]) = 1 * 6 = 6
- [1,3,1,2] from [1,3,1,2] has a total strength of min([1,3,1,2]) * sum([1,3,1,2]) = 1 * 7 = 7
The sum of all the total strengths is 1 + 9 + 1 + 4 + 4 + 4 + 3 + 5 + 6 + 7 = 44.
``````

Example 2:

``````Input: strength = [5,4,6]
Output: 213
Explanation: The following are all the contiguous groups of wizards:
-  from [5,4,6] has a total strength of min() * sum() = 5 * 5 = 25
-  from [5,4,6] has a total strength of min() * sum() = 4 * 4 = 16
-  from [5,4,6] has a total strength of min() * sum() = 6 * 6 = 36
- [5,4] from [5,4,6] has a total strength of min([5,4]) * sum([5,4]) = 4 * 9 = 36
- [4,6] from [5,4,6] has a total strength of min([4,6]) * sum([4,6]) = 4 * 10 = 40
- [5,4,6] from [5,4,6] has a total strength of min([5,4,6]) * sum([5,4,6]) = 4 * 15 = 60
The sum of all the total strengths is 25 + 16 + 36 + 36 + 40 + 60 = 213.
``````

Constraints:

• `1 <= strength.length <= 105`
• `1 <= strength[i] <= 109`
 `````` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 `````` ``````from itertools import accumulate class Solution: def totalStrength(self, strength: List[int]) -> int: mod = 10 ** 9 + 7 n = len(strength) # next small on the right right = [n] * n stack = [] for i in range(n): while stack and strength[stack[-1]] > strength[i]: right[stack.pop()] = i stack.append(i) # next small on the left left = [-1] * n stack = [] for i in range(n-1, -1, -1): while stack and strength[stack[-1]] >= strength[i]: left[stack.pop()] = i stack.append(i) # for each strength[i] as minimum, calculate sum total = 0 acc = list(accumulate(accumulate(strength), initial = 0)) for i in range(n): l, r = left[i], right[i] lacc = acc[i] - acc[max(l, 0)] racc = acc[r] - acc[i] ln, rn = i - l, r - i total += strength[i] * (racc * ln - lacc * rn) return total % mod``````