Problem: There are N holes in a two-dimensional plane. The coordinates of the i-th hole are (x_i,y_i).

Let R=10^{10^{10^{10}}}. Ringo performs the following operation:

* Randomly choose a point from the interior of a circle of radius R centered at the origin, and put Snuke there. Snuke will move to the hole with the smallest Euclidean distance from the point, and fall into that hole. If there are multiple such holes, the hole with the smallest index will be chosen.



For every i (1 \leq i \leq N), find the probability that Snuke falls into the i-th hole.

Here, the operation of randomly choosing a point from the interior of a circle of radius R is defined as follows:

* Pick two real numbers x and y independently according to uniform distribution on [-R,R].
* If x^2+y^2\leq R^2, the point (x,y) is chosen. Otherwise, repeat picking the real numbers x,y until the condition is met.

Constraints

* 2 \leq N \leq 100
* |x_i|,|y_i| \leq 10^6(1\leq i\leq N)
* All given points are pairwise distinct.
* All input values are integers.

Input

Input is given from Standard Input in the following format:


N
x_1 y_1
:
x_N y_N


Output

Print N real numbers. The i-th real number must represent the probability that Snuke falls into the i-th hole.

The output will be judged correct when, for all output values, the absolute or relative error is at most 10^{-5}.

Examples

Input

2
0 0
1 1


Output

0.5
0.5


Input

5
0 0
2 8
4 5
2 6
3 10


Output

0.43160120892732328768
0.03480224363653196956
0.13880483535586193855
0.00000000000000000000
0.39479171208028279727

Solution (in PYTHON3):

Solution:
import sys
input = sys.stdin.readline
import math

N = int(input())
XY = [list(map(int, input().split())) for _ in range(N)]

Theta = [[0, 0] for _ in range(N)]

line = True
for i in range(N-1):
    x1, y1 = XY[i]
    for j in range(i+1, N):
        x2, y2 = XY[j]
        for k in range(N):
            x3, y3 = XY[k]
            if (y1-y2)*(x1-x3) != (y1-y3)*(x1-x2):
                line = False
                break
    if line:
        break

if line:
    for i, (x1, y1) in enumerate(XY):
        max_x = True
        min_x = True
        max_y = True
        min_y = True
        for j, (x2, y2) in enumerate(XY):
            if i == j: continue
            if x1 <= x2:
                max_x = False
            if x2 <= x1:
                min_x = False
            if y1 <= y2:
                max_y = False
            if y2 <= y1:
                min_y = False
        if max_x or min_x or max_y or min_y:
            Theta[i][1] = math.pi
else:
    for i in range(N-1):
        x1, y1 = XY[i]
        for j in range(i+1, N):
            x2, y2 = XY[j]
            if x1 == x2:
                all_right = True
                all_left = True
                for k in range(N):
                    if k == i or k == j: continue
                    x3, y3 = XY[k]
                    if x3 > x1:
                        all_left = False
                    elif x3 < x1:
                        all_right = False
                if all_right:
                    if y1 > y2:
                        Theta[i][1] = math.pi
                        Theta[j][0] = math.pi
                    elif y1 < y2:
                        Theta[i][0] = math.pi
                        Theta[j][1] = math.pi
            else:
                all_up = True
                all_down = True
                for k in range(N):
                    if k == i or k == j: continue
                    x3, y3 = XY[k]
                    if (y3-y1)*(x1-x2) < (y1-y2)*(x3-x1):
                        if x1-x2 > 0:
                            all_up = False
                        elif x1-x2 < 0:
                            all_down = False
                    elif (y3-y1)*(x1-x2) > (y1-y2)*(x3-x1):
                        if x1-x2 > 0:
                            all_down = False
                        elif x1-x2 < 0:
                            all_up = False
                if all_down:
                    if x1 < x2:
                        theta = math.atan2(x2-x1, y1-y2)
                        Theta[i][0] = theta
                        Theta[j][1] = theta
                    else:
                        theta = math.atan2(x1-x2, y2-y1)
                        Theta[i][1] = theta
                        Theta[j][0] = theta
                if all_up:
                    if x1 < x2:
                        theta = math.atan2(x1-x2, y2-y1)
                        Theta[i][1] = theta
                        Theta[j][0] = theta
                    else:
                        theta = math.atan2(x2-x1, y1-y2)
                        Theta[i][0] = theta
                        Theta[j][1] = theta

for start, end in Theta:
    delta = end - start
    while delta < 0:
        delta += 2*math.pi
    while delta >= 2*math.pi:
        delta -= 2*math.pi
    print(delta/(2*math.pi))