# ---
# title: 1589. Maximum Sum Obtained of Any Permutation
# id: problem1589
# author: Tian Jun
# date: 2020-10-31
# difficulty: Medium
# categories: Greedy
# link: <https://leetcode.com/problems/maximum-sum-obtained-of-any-permutation/description/>
# hidden: true
# ---
# 
# We have an array of integers, `nums`, and an array of `requests` where
# `requests[i] = [starti, endi]`. The `ith` request asks for the sum of
# `nums[starti] + nums[starti + 1] + ... + nums[endi - 1] + nums[endi]`. Both
# `starti` and `endi` are _0-indexed_.
# 
# Return _the maximum total sum of all requests **among all permutations** of_
# `nums`.
# 
# Since the answer may be too large, return it **modulo** `109 + 7`.
# 
# 
# 
# **Example 1:**
# 
#     
#     
#     Input: nums = [1,2,3,4,5], requests = [[1,3],[0,1]]
#     Output: 19
#     Explanation: One permutation of nums is [2,1,3,4,5] with the following result: 
#     requests[0] -> nums[1] + nums[2] + nums[3] = 1 + 3 + 4 = 8
#     requests[1] -> nums[0] + nums[1] = 2 + 1 = 3
#     Total sum: 8 + 3 = 11.
#     A permutation with a higher total sum is [3,5,4,2,1] with the following result:
#     requests[0] -> nums[1] + nums[2] + nums[3] = 5 + 4 + 2 = 11
#     requests[1] -> nums[0] + nums[1] = 3 + 5  = 8
#     Total sum: 11 + 8 = 19, which is the best that you can do.
#     
# 
# **Example 2:**
# 
#     
#     
#     Input: nums = [1,2,3,4,5,6], requests = [[0,1]]
#     Output: 11
#     Explanation: A permutation with the max total sum is [6,5,4,3,2,1] with request sums [11].
# 
# **Example 3:**
# 
#     
#     
#     Input: nums = [1,2,3,4,5,10], requests = [[0,2],[1,3],[1,1]]
#     Output: 47
#     Explanation: A permutation with the max total sum is [4,10,5,3,2,1] with request sums [19,18,10].
# 
# 
# 
# **Constraints:**
# 
#   * `n == nums.length`
#   * `1 <= n <= 105`
#   * `0 <= nums[i] <= 105`
#   * `1 <= requests.length <= 105`
#   * `requests[i].length == 2`
#   * `0 <= starti <= endi < n`
# 
# 
## @lc code=start
using LeetCode

## add your code here:
## @lc code=end
