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:
from math import acos
pi = 3.14159265358979323846264338
N = int(input())
A = [[0, 0, 0, _] for _ in range(N)]
flg = [False for _ in range(N)]
for i in range(N):
    A[i][1], A[i][2] = map(int, input().split())
    A[i][0] = A[i][1] * A[i][1] + A[i][2] * A[i][2]
X = [[A[i][1], A[i][2]] for i in range(N)]
A.sort(reverse=True)
stx, sty = A[0][1], A[0][2]
px, py = stx, sty
flg[A[0][3]] = True
prev_point = A[0][3]
convex_hull = [A[0][3]]
while True:
    min_prod2 = [[1, 1], [N+1, N+1], 1]
    for i in range(N):
        for j in range(N):
            if i != prev_point and j != prev_point:
                ffflg = True
                dx1 = X[i][0] - px
                dx2 = X[j][0] - px
                dy1 = X[i][1] - py
                dy2 = X[j][1] - py
                inner_prod = dx1 * dx2 + dy1 * dy2
                norm1 = dx1 * dx1 + dy1 * dy1
                norm2 = dx2 * dx2 + dy2 * dy2
                sign = (inner_prod > 0) - (inner_prod < 0)
                if sign < min_prod2[2]:
                    min_prod2[0] = [inner_prod*inner_prod, norm1*norm2]
                    min_prod2[1] = [i, j]
                    min_prod2[2] = sign
                elif sign == min_prod2[2]:
                    if sign == 1:
                        if min_prod2[0][0] * norm1 * norm2 > inner_prod * inner_prod * min_prod2[0][1]:
                            min_prod2[0] = [inner_prod*inner_prod, norm1*norm2]
                            min_prod2[1] = [i, j]
                        elif min_prod2[0][0] * norm1 * norm2 == inner_prod * inner_prod * min_prod2[0][1]:
                            if min_prod2[0][1] > norm1 * norm2 or min_prod2[1] == [N+1, N+1]:
                                min_prod2[0] = [inner_prod*inner_prod, norm1*norm2]
                                min_prod2[1] = [i, j]
                    elif sign == 0:
                        if min_prod2[0][1] > norm1 * norm2 or min_prod2[1] == [N+1, N+1]:
                            min_prod2[0] = [inner_prod*inner_prod, norm1*norm2]
                            min_prod2[1] = [i, j]
                    else:
                        if min_prod2[0][0] * norm1 * norm2 < inner_prod * inner_prod * min_prod2[0][1]:
                            min_prod2[0] = [inner_prod*inner_prod, norm1*norm2]
                            min_prod2[1] = [i, j]
                        elif min_prod2[0][0] * norm1 * norm2 == inner_prod * inner_prod * min_prod2[0][1]:
                            if min_prod2[0][1] > norm1 * norm2 or min_prod2[1] == [N+1, N+1]:
                                min_prod2[0] = [inner_prod*inner_prod, norm1*norm2]
                                min_prod2[1] = [i, j]
    if flg[min_prod2[1][0]] and flg[min_prod2[1][1]]:
        break
    else:
        if flg[min_prod2[1][0]] and not flg[min_prod2[1][1]]:
            prev_point = min_prod2[1][1]
        elif not flg[min_prod2[1][0]] and flg[min_prod2[1][1]]:
            prev_point = min_prod2[1][0]
        elif not flg[min_prod2[1][0]] and not flg[min_prod2[1][1]]:
            prev_point = min_prod2[1][0]
        convex_hull.append(prev_point)
        flg[prev_point] = True
        px, py = X[prev_point][0], X[prev_point][1]
M = len(convex_hull)
prob = [0 for _ in range(N)]
for i in range(M):
    center = convex_hull[i]
    ii, jj = convex_hull[(i-1)%M], convex_hull[(i+1)%M]
    dx1 = X[ii][0] - X[center][0]
    dx2 = X[jj][0] - X[center][0]
    dy1 = X[ii][1] - X[center][1]
    dy2 = X[jj][1] - X[center][1]
    ip = dx1 * dx2 + dy1 * dy2
    n1 = dx1 * dx1 + dy1 * dy1
    n2 = dx2 * dx2 + dy2 * dy2
    n1 = n1**0.5
    n2 = n2**0.5
    prob[center] = 0.5 - (acos((ip/n1)/n2))/(2*pi)
for i in range(N):
    print(prob[i])