Description: 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 Format: 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 Format: 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. Note: None