Sunlight

Roman tenancy law recognized a right to sunlight for every resident, whatever their status. Many of the health benefits of good sun exposure were already known back then.

A city plan reviewer therefore starts by measuring how the proposed buildings divide that resource. An avenue runs from west to east and carries $N$ buildings. The $i$-th building from the west stands at position $X_i$, is $H_i$ meters tall, and is infinitesimally thin.

The sky covers 180 degrees, from the western horizon to the eastern horizon, and the sun crosses those 180 degrees at a constant rate over 12 hours. Look at the sky from the top of building $i$, the point $(X_i, H_i)$. Another building $j$ hides the sky from the horizon on its own side up to the direction of its top $(X_j, H_j)$. If that direction points below the horizontal, building $j$ hides no sky at all. When $A$ degrees of sky are left uncovered, the top of building $i$ is in sunlight for $12A/180$ hours.

Find how long the top of each building is in sunlight.

The first line contains the number of buildings $N$ ($1 \le N \le 2 \times 10^5$).

Each of the next $N$ lines contains two integers $X_i$ and $H_i$ ($1 \le X_i, H_i \le 10^9$), the position and the height of one building in meters. The buildings are listed from west to east, so $X_1 < X_2 < \cdots < X_N$.

Print $N$ lines. On the $i$-th line, print how many hours the top of the $i$-th building is in sunlight, rounded to six decimal places.