Adding Fractions

You have discovered a new way to add fractions ! Now, the result of adding fractions a/b and c/d is (a + c)/(b + d). Similarly the result of adding 3 fractions a/b, c/d, e/f is (a + c + e)/(b + d + f), and so on. You are given a list of N fractions a_1/b_1, a_2/b_2,...,a_N/b_N. You wonder what for each fraction i is the maximum fraction that you can obtain by adding together some continuous fracti