You are given a positive integer array grades which represents the grades of students in a university. You would like to enter all these students into a competition in ordered non-empty groups, such that the ordering meets the following conditions:
ith group is less than the sum of the grades of students in the (i + 1)th group, for all groups (except the last).ith group is less than the total number of students in the (i + 1)th group, for all groups (except the last).Return the maximum number of groups that can be formed.
Example 1:
Input: grades = [10,6,12,7,3,5] Output: 3 Explanation: The following is a possible way to form 3 groups of students: - 1st group has the students with grades = [12]. Sum of grades: 12. Student count: 1 - 2nd group has the students with grades = [6,7]. Sum of grades: 6 + 7 = 13. Student count: 2 - 3rd group has the students with grades = [10,3,5]. Sum of grades: 10 + 3 + 5 = 18. Student count: 3 It can be shown that it is not possible to form more than 3 groups.
Example 2:
Input: grades = [8,8] Output: 1 Explanation: We can only form 1 group, since forming 2 groups would lead to an equal number of students in both groups.
Constraints:
1 <= grades.length <= 1051 <= grades[i] <= 105