Tourist is a very curious person by nature. He has a infinite square notebook, on the $i^{th}$ page of the notebook he writes the number of ways he can write i as sum of the area of two squares having integral side lengths. As he is eternal he will keep writing such sum on each day till infinity. His friend Umnik is very curious to find out what the sum of numbers written on all these pages would be. Since the number can be too large, he wants to find the sum of numbers on each page divided by Tourist's lifespan. Mathematically, if F(i) is the number written on each page, he wants to find $\lim_{n\to\infty}((\sum_{i=1}^{n}F(i))/n)$ Help Umnik in finding this number. Let this answer be $x$, report the integer part of $(x*10^{12})$.