Let N=100^{2}+99^{2}-98^{2}-97^{2}+96^{2}+\cdots+4^{2}+3^{2}-2^{2}-1^{2}, where the additions and subtractions alternate in pairs. Find the remainder when N is divided by 1000 .
Let N=100^{2}+99^{2}-98^{2}-97^{2}+96^{2}+\cdots+4^{2}+3^{2}-2^{2}-1^{2}, where the additions and subtractions alternate in pairs. Find the remainder when N is divided by 1000 .