You are given a 0-indexed integer array nums. You are allowed to permute nums into a new array perm of your choosing.

We define the greatness of nums be the number of indices 0 <= i < nums.length for which perm[i] > nums[i].

Return the maximum possible greatness you can achieve after permuting nums.

 

Example 1:

Input: nums = [1,3,5,2,1,3,1]
Output: 4
Explanation: One of the optimal rearrangements is perm = [2,5,1,3,3,1,1].
At indices = 0, 1, 3, and 4, perm[i] > nums[i]. Hence, we return 4.

Example 2:

Input: nums = [1,2,3,4]
Output: 3
Explanation: We can prove the optimal perm is [2,3,4,1].
At indices = 0, 1, and 2, perm[i] > nums[i]. Hence, we return 3.

 

Constraints:

• 1 <= nums.length <= 105
• 0 <= nums[i] <= 109