C. Torn Lucky Ticket
time limit per test
2 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output

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.

Input

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 $9$.

Output

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.

Examples
Input
105 93746 59 3746 593 746 5937 46 59374 6
Output
20

Input
52 22 222 2222 22222
Output
13

Input
31 1 1
Output
9