p03428 AtCoder Grand Contest 021 - Holes
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
```python
"""
@ 凸包をつくる
    > 凸包内部の点に属する領域は、半径Rの円からするともはやないものとして考えて良い
    > というかこの多角形自体点として考えていい！
@ 凸包の頂点vについて
    > vの両隣との傾きだけあればよい
    > その間の角度 / 360が答え
"""

from math import gcd, atan, pi, degrees

def cross3(a, b, c):
    return (b[0]-a[0])*(c[1]-a[1]) - (b[1]-a[1])*(c[0]-a[0])

def convex_hull(ps):
    qs = []
    N = len(ps)
    for p in ps:
        # 一直線上で高々2点にする場合は ">=" にする
        while len(qs) > 1 and cross3(qs[-1], qs[-2], p) > 0:
            qs.pop()
        qs.append(p)
    t = len(qs)
    for i in range(N-2, -1, -1):
        p = ps[i]
        while len(qs) > t and cross3(qs[-1], qs[-2], p) > 0:
            qs.pop()
        qs.append(p)
    return qs

def tup_to_key(tup):
    x, y = tup
    x += 10 ** 7
    y += 10 ** 7
    x *= 10 ** 8
    return x + y

def key_to_tup(key):
    x, y = divmod(key, 10 ** 8)
    x -= 10 ** 7
    y -= 10 ** 7
    return x, y

def angle(x1, y1, x2, y2):
    if y1 == y2:
        return pi / 2
    return atan(-(x1 - x2) / (y1 - y2))

def on_line(ps):
    st = set()
    for p, q in zip(ps, ps[1:]):
        px, py = p
        qx, qy = q
        dx, dy = qx - px, qy - py
        g = gcd(dx, dy)
        dx //= g
        dy //= g
        st.add(tup_to_key((dx, dy)))
    return len(st) == 1

if __name__ == "__main__":
    N = int(input())
    if N == 2:
        print(0.5)
        print(0.5)
        exit(0)

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

    # ps = sorted(points)
    # for a, b in zip(ps, ps[1:]):
    #     x1, y1 = a
    #     x2, y2 = b
    #     x, y = x2 - x1, y2 - y1
    #     print(x, y)

    if on_line(sorted(points)):
        mn = min(points)
        mx = max(points)
        res[tup_to_key(mn)] = 0.5
        res[tup_to_key(mx)] = 0.5
    else:
        ps = convex_hull(sorted(points))[:-1]
        sz = len(ps)
        for i, (x, y) in enumerate(ps):
            key = tup_to_key((x, y))
            lx, ly = ps[i - 1]
            rx, ry = ps[(i + 1) % sz]
            la = angle(x, y, lx, ly)
            ra = angle(x, y, rx, ry)
            a = ra - la
            # a = min(a, 2 * pi - a)
            # print(x, y)
            # print(degrees(la), degrees(ra))
            if a < 0:
                a += pi
            # print(la, ra)
            res[key] = a / (2 * pi)

    for tup in points:
        key = tup_to_key(tup)
        if key in res:
            print(res[key])
        else:
            print(0)

```