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Count Different Palindromic Subsequences

Given a string s, return the number of different non-empty palindromic subsequences in s.

Given a string s, return the number of different non-empty palindromic subsequences in s. Since the answer may be very large, return it modulo 10^9 + 7.

A subsequence of a string is obtained by deleting zero or more characters from the string.

A sequence is palindromic if it is equal to the sequence reversed.

Two sequences a1, a2, ... and b1, b2, ... are different if there is some i for which ai != bi.

Count Different Palindromic Subsequences diagram

Example 1

Input: s = "bccb"

Output: 6

Explanation: The 6 different non-empty palindromic subsequences are 'b', 'c', 'bb', 'cc', 'bcb', 'bccb'. Note that 'bcb' is counted only once, even though it occurs twice.

Example 2

Input: s = "abcdabcdabcdabcdabcdabcdabcdabcddcbadcbadcbadcbadcbadcbadcbadcba"

Output: 104860361

Explanation: There are 3104860382 different non-empty palindromic subsequences, which is 104860361 modulo 10^9 + 7.

Constraints

  • 1 <= s.length <= 1000
  • s[i] is either 'a', 'b', 'c', or 'd'.

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