Fast Squarier Transform

Input

The first line of the input contains $2$ integers $n,m$ (1 \leq n, m \leq 10^5).

The second line of the input contains $n$ integers a_1, a_2, \dots, a_n (0 \le a_i, a_1 + a_2 + \ldots + a_n \le 2\cdot 10^7).

The third line of the input contains $m$ integers b_1, b_2, \dots, b_m (0 \le b_i, b_1 + b_2 + \ldots + b_m \le 2\cdot 10^7).

Output

Print a single integer — the sum from the statement.

Examples

Note

In the first sample the answer is \lfloor \sqrt{|1 - 2|} \rfloor + \lfloor \sqrt{|1 - 3|} \rfloor = \lfloor \sqrt{1} \rfloor + \lfloor \sqrt{2} \rfloor = 1 + 1 = 2.

In the second sample, the answer is \lfloor \sqrt{|1 - 3|} \rfloor + \lfloor \sqrt{|1 - 4|} \rfloor + \lfloor \sqrt{|1 - 5|} \rfloor + \lfloor \sqrt{|2 - 3|} \rfloor + \lfloor \sqrt{|2 - 4|} \rfloor + \lfloor \sqrt{|2 - 5|} \rfloor = \lfloor \sqrt{2} \rfloor + \lfloor \sqrt{3} \rfloor + \lfloor \sqrt{4} \rfloor + \lfloor \sqrt{1} \rfloor + \lfloor \sqrt{2} \rfloor + \lfloor \sqrt{3} \rfloor = 1 + 1 + 2 + 1 + 1 + 1 = 7.