Fast Squarier Transform

You are given two arrays of integers $[a_1,a_2,\dots ,a_n]$ and $[b_1,b_2,\dots ,b_m]$.

Find the following value:

Note that $\lfloor x\rfloor$ denotes the maximum integer not exceeding $x$, and $|x|$ denotes the absolute value of $x$.

Input

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

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

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

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 $\lfloor \sqrt{|1-3|}\rfloor +\lfloor \sqrt{|1-4|}\rfloor +\lfloor \sqrt{|1-5|}\rfloor +\lfloor \sqrt{|2-3|}\rfloor +\lfloor \sqrt{|2-4|}\rfloor +\lfloor \sqrt{|2-5|}\rfloor =$ $\lfloor \sqrt{2}\rfloor +\lfloor \sqrt{3}\rfloor +\lfloor \sqrt{4}\rfloor +\lfloor \sqrt{1}\rfloor +\lfloor \sqrt{2}\rfloor +\lfloor \sqrt{3}\rfloor =1+1+2+1+1+1=7$.