> For the complete documentation index, see [llms.txt](https://jaywin.gitbook.io/leetcode/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://jaywin.gitbook.io/leetcode/solutions/2002-maximum-product-of-the-length-of-two-palindromic-subsequences.md).

# 2002. Maximum Product of the Length of Two Palindromic Subsequences

<https://leetcode.com/problems/maximum-product-of-the-length-of-two-palindromic-subsequences>

## Description

Given a string `s`, find two **disjoint palindromic subsequences** of `s` such that the **product** of their lengths is **maximized**. The two subsequences are **disjoint** if they do not both pick a character at the same index.

Return *the **maximum** possible **product** of the lengths of the two palindromic subsequences*.

A **subsequence** is a string that can be derived from another string by deleting some or no characters without changing the order of the remaining characters. A string is **palindromic** if it reads the same forward and backward.

**Example 1:**

![example-1](https://assets.leetcode.com/uploads/2021/08/24/two-palindromic-subsequences.png)

```
**Input:** s = "leetcodecom"
**Output:** 9
**Explanation**: An optimal solution is to choose "ete" for the 1st subsequence and "cdc" for the 2nd subsequence.
The product of their lengths is: 3 * 3 = 9.
```

**Example 2:**

```
**Input:** s = "bb"
**Output:** 1
**Explanation**: An optimal solution is to choose "b" (the first character) for the 1st subsequence and "b" (the second character) for the 2nd subsequence.
The product of their lengths is: 1 * 1 = 1.
```

**Example 3:**

```
**Input:** s = "accbcaxxcxx"
**Output:** 25
**Explanation**: An optimal solution is to choose "accca" for the 1st subsequence and "xxcxx" for the 2nd subsequence.
The product of their lengths is: 5 * 5 = 25.
```

**Constraints:**

* `2 <= s.length <= 12`
* `s` consists of lowercase English letters only.

## ac

```java
```