CEOI '17 P5 - Palindromic Partitions

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Points: 15 (partial)
Time limit: 4.5s
Memory limit: 128M

Problem types

A partition of a string s is a set of one or more non-overlapping non-empty substrings of s (call them a_1, a_2, \dots, a_d), such that s is their concatenation: s = a_1 + a_2 + \dots + a_d. We call these substrings "chunks" and define the length of such a partition to be the number of chunks, d.

We can represent the partition of a string by writing each chunk in parentheses. For example, the string "decode" can be partitioned as (d)(ec)(ode) or (d)(e)(c)(od)(e) or (decod)(e) or (decode) or (de)(code) or a number of other ways.

A partition is palindromic if its chunks form a palindrome when we consider each chunk as an atomic unit. For example, the only palindromic partitions of "decode" are (de)(co)(de) and (decode). This also illustrates that every word has a trivial palindromic partition of length one.

Your task is to compute the maximal possible number of chunks in palindromic partition.


The input starts with the number of test cases t in the first line. The following t lines describe individual test cases consisting of a single word s, containing only lowercase letters of the English alphabet. There are no spaces in the input.


For every test case, output a single number: the length of the longest palindromic partition of the input word s.


Let us denote the length of the input string s with n.

  • 1 \le t \le 10
  • 1 \le n \le 10^6
Subtask 1 (15%)
  • n \le 30
Subtask 2 (20%)
  • n \le 300
Subtask 3 (25%)
  • n \le 10\,000
Subtask 4 (40%)
  • no additional constraints

Sample Input 1


Sample Output 1



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