##### Transform to Palindrome: Hackerrank

The Orion alphabet system consists of letters, denoted by the integers from to . The Orion letter is denoted by the integer .

Some Orion letters can be transformed to other Orion letters. A transformation is denoted by a pair of two Orion letters, . Using this transformation, you can replace letter with letter .

Transformations also have additional properties:

- If letter can be transformed to letter using a transformation, then letter can be transformed to letter as well.
- If letter can be transformed to letter and letter can be transformed to letter , then letter can be transformed to letter as well.

You are given a sequence comprising of Orion letters. You are given transformations that can be applied to . You may apply transformations to zero or more letters in the sequence. When a transformation is applied to a letter, the other letters of the string remain unaffected. You can also apply a single transformation multiple times on the same sequence.

Print the length of the *longest possible palindromic subsequence* after applying zero or more transformations on the letters of the given sequence.

For example, in the sequence below, transformation is first applied to the sequence to obtain . The *longest palindrome subsequence* is then obtained from the resulting *transformed sequence* by removing letter .

**Input Format**

The first line contains three space separated integers , and . The following lines each contain two space separated integers and , denoting a transformation from letter to letter . The last line contains positive integers (elements of the string).

**Constraints**

**Output Format**

Print a single line containing an integer denoting the length of the *longest possible palindromic subsequence* which can be obtained after applying transformations on the given string.

**Sample Input 0**

```
10 7 6
1 3
5 7
3 5
2 6
2 4
8 4
10 9
1 9 2 3 10 3
```

**Sample Output 0**

```
5
```

**Explanation 0**

The given string is . After transforming the last letter from to , string becomes . After transforming to , string becomes . One of the longest palindromic subsequence is formed as follows .

**Sample Input 1**

```
10 8 15
1 2
1 3
2 7
3 1
4 5
6 8
9 6
10 5
1 4 5 7 9 8 1 3 10 4 5 10 2 7 8
```

**Sample Output 1**

```
10
```

**Explanation 1**

After performing various transformations, the following string can be obtained . One of the longest palindromic subsequence is

**Solution**

`Working on the solution.`