p01556 ConvexCut
A convex polygon consisting of N vertices is given. The coordinates of each vertex are represented counterclockwise by (X1, Y1), (X2, Y2), ……, (XN, YN). No matter what straight line passes through the point P, find the coordinates of the point P so that the areas of the two convex polygons obtained after cutting are equal.

Constraints

* All inputs are integers

* 3 ≤ N ≤ 50

* 0 ≤ | Xi |, | Yi | ≤ 1000000

* The input polygon is a simple convex polygon.

* The output must satisfy max (| X-cX |, | Y-cY |) ≤ 0.0001 when the output coordinates are (X, Y) and the exact solution is (cX, cY).

Input

The input is given in the following format.

> N
> X1 Y1
> X2 Y2
> ……
> XN YN
>

Output

If there is a point that satisfies the condition of the problem statement, the coordinates of that point

> X Y
>

Output in the format of. If the point does not exist, output "NA" on one line.

Examples

Input

4
100 100
0 100
0 0
100 0


Output

50.00000 50.00000


Input

3
100 100
0 100
0 0


Output

NA
```python
import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time,copy,functools

sys.setrecursionlimit(10**7)
inf = 10**20
eps = 1.0 / 10**13
mod = 10**9+7
dd = [(-1,0),(0,1),(1,0),(0,-1)]
ddn = [(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]

def LI(): return [int(x) for x in sys.stdin.readline().split()]
def LI_(): return [int(x)-1 for x in sys.stdin.readline().split()]
def LF(): return [float(x) for x in sys.stdin.readline().split()]
def LS(): return sys.stdin.readline().split()
def I(): return int(sys.stdin.readline())
def F(): return float(sys.stdin.readline())
def S(): return input()
def pf(s): return print(s, flush=True)

def area(xy):
    xy = sorted(xy)
    x = [xy[i][0] - xy[0][0] for i in range(3)]
    y = [xy[i][1] - xy[0][1] for i in range(3)]
    return abs(x[1]*y[2] - x[2]*y[1]) / 2

def ccw(a, b, c):
    ax = b[0] - a[0]
    ay = b[1] - a[1]
    bx = c[0] - a[0]
    by = c[1] - a[1]
    t = ax*by - ay*bx;
    if t > 0:
        return 1
    if t < 0:
        return -1
    if ax*bx + ay*by < 0:
        return 2
    if ax*ax + ay*ay < bx*bx + by*by:
        return -2
    return 0

def convex_hull(ps):
    n = len(ps)
    k = 0
    ps.sort()
    ch = [None] * (n*2)
    for i in range(n):
        while k >= 2 and ccw(ch[k-2], ch[k-1], ps[i]) <= 0:
            k -= 1
        ch[k] = ps[i]
        k += 1
    t = k + 1
    for i in range(n-2,-1,-1):
        while k >= t and ccw(ch[k-2], ch[k-1], ps[i]) <= 0:
            k -= 1
        ch[k] = ps[i]
        k += 1

    return ch[:k-1]

def bs(f, mi, ma):
    mm = -1
    while ma > mi + eps:
        mm = (ma+mi) / 2.0
        if f(mm):
            mi = mm + eps
        else:
            ma = mm
    if f(mm):
        return mm + eps
    return mm

def intersection(a1, a2, b1, b2):
    x1,y1 = a1
    x2,y2 = a2
    x3,y3 = b1
    x4,y4 = b2

    ksi = (y4 - y3) * (x4 - x1) - (x4 - x3) * (y4 - y1)
    eta = (x2 - x1) * (y4 - y1) - (y2 - y1) * (x4 - x1)
    delta = (x2 - x1) * (y4 - y3) - (y2 - y1) * (x4 - x3)
    if delta == 0:
        return None
    ramda = ksi / delta;
    mu = eta / delta;
    if ramda >= 0 and ramda <= 1 and mu >= 0 and mu <= 1:
        return (x1 + ramda * (x2 - x1), y1 + ramda * (y2 - y1))

    return None

def main():
    n = I()
    a = convex_hull([LI() for _ in range(n)])
    n = len(a)
    a = a + a + a
    s = 0
    for i in range(1,n-1):
        s += area([a[0],a[i],a[i+1]])
    def f(i, fk):
        t = 0
        tj = i + 1
        ra = [a[i+1][j] - a[i][j] for j in range(2)]
        ap = [a[i][j] + ra[j] * fk for j in range(2)]
        for j in range(i+1, i+n):
            u = area([ap, a[j], a[j+1]])
            if t + u >= s / 2:
                tj = j
                break
            t += u
        ts = s / 2 - t
        sa = [a[tj+1][j] - a[tj][j] for j in range(2)]
        def _f(k):
            b = [a[tj][j] + sa[j] * k for j in range(2)]
            fs = area([a[i], a[tj], b])
            return fs < ts
        bk = bs(_f, 0, 1)
        return [ap, [a[tj][j] + sa[j] * bk for j in range(2)]]

    ls = [f(i//5, random.random()) for i in range(n*5)]
    ll = len(ls)
    kts = []
    sx = 0
    sy = 0
    for i in range(ll):
        for j in range(i+1,ll):
            t = intersection(ls[i][0], ls[i][1], ls[j][0], ls[j][1])
            if t is None:
                return 'NA'
            kts.append(t)
            sx += t[0]
            sy += t[1]
    mx = sx / len(kts)
    my = sy / len(kts)
    keps = 1.0 / 10**5
    for i in range(len(kts)):
        if abs(mx-t[0]) > keps or abs(my-t[1]) > keps:
            return 'NA'
    return '{:.9f} {:.9f}'.format(mx, my)



print(main())


```