A16333 | Torn Lucky Ticket

A ticket is a non-empty string of digits from $1$ to $9$ .

A lucky ticket is such a ticket that:

- it has an even length;
- the sum of digits in the first half is equal to the sum of digits in the second half.

You are given $n$ ticket pieces $s_1, s_2, \dots, s_n$ . How many pairs $(i, j)$ (for $1 \le i, j \le n$ ) are there such that $s_i + s_j$ is a lucky ticket? Note that it's possible that $i=j$ .

Here, the + operator denotes the concatenation of the two strings. For example, if $s_i$ is 13, and $s_j$ is 37, then $s_i + s_j$ is 1337.

The first line contains a single integer $n$ ( $1 \le n \le 2 \cdot 10^5$ ) — the number of ticket pieces.

The second line contains $n$ non-empty strings $s_1, s_2, \dots, s_n$ , each of length at most $5$ and consisting only of digits from $1$ to $9$ .

Print a single integer — the number of pairs $(i, j)$ (for $1 \le i, j \le n$ ) such that $s_i + s_j$ is a lucky ticket.