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.
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Example 1:
\n\n\nInput: grades = [10,6,12,7,3,5]\nOutput: 3\nExplanation: The following is a possible way to form 3 groups of students:\n- 1st group has the students with grades = [12]. Sum of grades: 12. Student count: 1\n- 2nd group has the students with grades = [6,7]. Sum of grades: 6 + 7 = 13. Student count: 2\n- 3rd group has the students with grades = [10,3,5]. Sum of grades: 10 + 3 + 5 = 18. Student count: 3\nIt can be shown that it is not possible to form more than 3 groups.\n\n\n
Example 2:
\n\n\nInput: grades = [8,8]\nOutput: 1\nExplanation: We can only form 1 group, since forming 2 groups would lead to an equal number of students in both groups.\n\n\n
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Constraints:
\n\n1 <= grades.length <= 1051 <= grades[i] <= 105给你一个正整数数组 grades ，表示大学中一些学生的成绩。你打算将 所有 学生分为一些 有序 的非空分组，其中分组间的顺序满足以下全部条件：
i 个分组中的学生总成绩 小于 第 (i + 1) 个分组中的学生总成绩，对所有组均成立（除了最后一组）。i 个分组中的学生总数 小于 第 (i + 1) 个分组中的学生总数，对所有组均成立（除了最后一组）。返回可以形成的 最大 组数。
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示例 1：
\n\n输入：grades = [10,6,12,7,3,5]\n输出：3\n解释：下面是形成 3 个分组的一种可行方法：\n- 第 1 个分组的学生成绩为 grades = [12] ，总成绩：12 ，学生数：1\n- 第 2 个分组的学生成绩为 grades = [6,7] ，总成绩：6 + 7 = 13 ，学生数：2\n- 第 3 个分组的学生成绩为 grades = [10,3,5] ，总成绩：10 + 3 + 5 = 18 ，学生数：3 \n可以证明无法形成超过 3 个分组。\n\n\n
示例 2：
\n\n输入：grades = [8,8]\n输出：1\n解释：只能形成 1 个分组，因为如果要形成 2 个分组的话，会导致每个分组中的学生数目相等。\n\n\n
\n\n
提示：
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