Find Maximum Maxima Count

For each non-empty prefix of the original string, every character whose count reaches the maximum count in that prefix gets 1, including all tied characters. Find the maximum accumulated count of a single character.

输入格式

One line with a lowercase string, 1≤length≤100000.

输出格式

Output a single integer answer.

样例 1

输入：

bccaaacb

输出：

6

样例 2

输入：

zzzz

输出：

4

样例 3

输入：

ab

输出：

2

样例说明

Example 1: c is tied for or holds the maximum in prefixes 2, 3, 4, 5, 7 and 8, 6 times in total. Example 2: z is the maximum in all 4 prefixes, so the answer is 4. Example 3: a is the maximum in both a and ab, while b is the maximum only in ab, so the answer is 2.