101755: [AtCoder]ABC175 F - Making Palindrome

Problem Statement

We have $N$ strings of lowercase English letters: $S_1, S_2, \cdots, S_N$.

Takahashi wants to make a string that is a palindrome by choosing one or more of these strings - the same string can be chosen more than once - and concatenating them in some order of his choice.

The cost of using the string $S_i$ once is $C_i$, and the cost of using it multiple times is $C_i$ multiplied by that number of times.

Find the minimum total cost needed to choose strings so that Takahashi can make a palindrome.

If there is no choice of strings in which he can make a palindrome, print $-1$.

Constraints

• $1 \leq N \leq 50$
• $1 \leq |S_i| \leq 20$
• $S_i$ consists of lowercase English letters.
• $1 \leq C_i \leq 10^9$

Input

Input is given from Standard Input in the following format:

$N$
$S_1$ $C_1$
$S_2$ $C_2$
$:$
$S_N$ $C_N$

Output

Print the minimum total cost needed to choose strings so that Takahashi can make a palindrome, or $-1$ if there is no such choice.

Sample Input 1

3
ba 3
abc 4
cbaa 5

Sample Output 1

7

We have ba, abc, and cbaa.

For example, we can use ba once and abc once for a cost of $7$, then concatenate them in the order abc, ba to make a palindrome. Also, we can use abc once and cbaa once for a cost of $9$, then concatenate them in the order cbaa, abc to make a palindrome.

We cannot make a palindrome for a cost less than $7$, so we should print $7$.

Sample Input 2

2
abcab 5
cba 3

Sample Output 2

11

We can choose abcab once and cba twice, then concatenate them in the order abcab, cba, cba to make a palindrome for a cost of $11$.

Sample Input 3

4
ab 5
cba 3
a 12
ab 10

Sample Output 3

8

We can choose a once, which is already a palindrome, but it is cheaper to concatenate ab and cba.

Sample Input 4

2
abc 1
ab 2

Sample Output 4

-1

We cannot make a palindrome, so we should print $-1$.