Problem: Problem

Satake doesn't like being bent.
For example, I don't like pencils, chopsticks, and bent-shaped houses, and I don't like taking actions such as turning right or left.

By the way, Satake who lives on the XY plane is $ N $ shops $ (X_ {1}, Y_ {1}), (X_ {2}, Y_ {2}), \ ldots, (X_ {N} , Y_ {N}) I was asked to shop for $. Depart from the house at coordinates $ (0, 0) $ in the direction of $ (1, 0) $, shop at all stores, and then return home. You can go around the shops in any order. As a user, Satake can perform any of the following actions as many times as you like.

1. Go as much as you like in the direction you are facing
2. When the coordinates are the same as the shop or house, rotate clockwise or counterclockwise by the desired angle on the spot.
3. When the coordinates are the same as the store, shop while maintaining the coordinates and the direction in which they are facing.



As I said earlier, Satake doesn't like to bend. To prepare your mind, find the minimum sum of the angles that Satake will rotate in Action 2. As an example, if you rotate $ 90 ^ {\ circ} $ clockwise and then $ 90 ^ {\ circ} $ counterclockwise, the sum of the angles will be $ 180 ^ {\ circ} $.

Constraints

The input meets the following conditions:

* $ 2 \ le N \ le 8 $
* $ -1000 \ le X_ {i}, Y_ {i} \ le 1000 \ quad (1 \ le i \ le N) $
* $ (X_ {i}, Y_ {i}) \ ne (0, 0) \ quad (1 \ le i \ le N) $
* $ (X_ {i}, Y_ {i}) \ ne (X_ {j}, Y_ {j}) \ quad (i \ ne j) $
* All inputs are integers

Input

The input is given in the following format:


$ N $
$ X_ {1} $ $ Y_ {1} $
$ \ vdots $
$ X_ {N} $ $ Y_ {N} $


The input consists of $ N + 1 $ lines.
The $ 1 $ line is given $ N $, which represents the number of stores to shop.
The $ N $ line starting from the $ 2 $ line is given the coordinates $ X_ {i}, Y_ {i} $ of the store where you shop, separated by blanks.

Output

Please output the minimum value of the sum of the angles that Satake rotates in degrees. However, the correct answer is given only when the absolute error from the assumed solution is $ 10 ^ {-4} $ or less.

Examples

Input

2
0 1
0 -1


Output

450.00000000


Input

3
1 0
0 1
-2 -1


Output

386.565051

Solution (in CPP):

Solution:
#include<iostream>
#include<vector>
#include<iomanip>
#include<cmath>
#include<algorithm>
#include<cassert>
using namespace std;

#define EPS (1e-10)
#define equals(a, b) (fabs((a) - (b)) < EPS)

struct Point;
typedef Point Vector;
typedef vector<Point> Polygon;
struct Circle;
struct Segment;
typedef Segment Line;
double norm(Point a);
double abs(Point a);
double dot(Vector a, Vector b);
double cross(Vector a, Vector b);
double getDistance(Point a, Point b);
double getDistanceLP(Line l, Point p);
double getDistanceSP(Segment s, Point p);
double getDistance(Segment s1, Segment s2);
bool isOrthogonal(Vector a, Vector b);
bool isOrthogonal(Point a1, Point a2, Point b1, Point b2);
bool isOrthogonal(Segment s1, Segment s2);
bool isParallel(Vector a, Vector b);
bool isParallel(Point a1, Point a2, Point b1, Point b2);
bool isParallel(Segment s1, Segment s2);
int ccw(Point p0, Point p1, Point p2);
bool intersect(Point p1, Point p2, Point p3, Point p4);
bool intersect(Segment s1, Segment s2);
bool intersect(Circle c, Line l); // 誤差の検証をしていない
bool intersect(Circle c1, Circle c2); // 誤差の検証をしていない

Point project(Segment s, Point p);
Point reflect(Segment s, Point p);
Point getCrossPoint(Segment s1, Segment s2);
pair<Point,Point> getCrossPoints(Circle c, Line l);
pair<Point,Point> getCrossPoints(Circle c1, Circle c2); // 誤差の検証をしていない
pair<Point,Point> getContactPoints(Circle c, Point p); // 接点 点は円の外部

double area(Polygon g); // convexでなくてもよい. absを消せば符号付き面積
bool isConvex(Polygon g); // O(n^2) 線形時間アルゴリズムが存在するらしい
int contains(Polygon g, Point p);

double arg(Vector p);   // 偏角
Vector polar(double a, double r); // 極座標系->ベクトル

Polygon andrewScan(Polygon g); // 凸包の辺上の点も含めたければ!=CLOCKWISEを==COUNTER_CLOCKWISEに
double convexDiameter(Polygon g); // gはconvex 


struct Point{
    double x, y;

    Point(double x = 0, double y = 0) : x(x), y(y) {}

    Point operator + (Point p){ return Point(x+p.x, y+p.y); }
    Point operator - (Point p){ return Point(x-p.x, y-p.y); }
    Point operator * (double a){ return Point(a*x, a*y); }
    Point operator / (double a){ return Point(x/a, y/a); }

    double abs() { return sqrt(norm()); }
    double norm() { return x*x + y*y; }

    bool operator < (const Point &p) const{
        return x != p.x ? x < p.x : y < p.y;
    }

    bool operator == (const Point &p) const{
        return fabs(x-p.x) < EPS && fabs(y-p.y) < EPS;
    }
};

typedef Point Vector;
typedef vector<Point> Polygon;

struct Circle{
    Point c;
    double r;
    Circle(Point c = Point(), double r = 0.0) : c(c), r(r) {}
};

struct Segment{
    Point p1, p2;
    Segment(Point p1, Point p2) : p1(p1), p2(p2) {}
};

typedef Segment Line;


double norm(Point a){
    return a.x * a.x + a.y * a.y;
}

double abs(Point a){
    return sqrt(norm(a));
}

double dot(Vector a, Vector b){
    return a.x * b.x + a.y * b.y;
}

double cross(Vector a, Vector b){
    return a.x * b.y - a.y * b.x;
}

double getDistance(Point a, Point b){
    return abs(a - b);
}

double getDistanceLP(Line l, Point p){
    return abs(cross(l.p2 - l.p1, p - l.p1) / abs(l.p2 - l.p1));
}

double getDistanceSP(Segment s, Point p){
    if(dot(s.p2-s.p1, p-s.p1) < 0.0)    return abs(p-s.p1);
    if(dot(s.p1-s.p2, p-s.p2) < 0.0)    return abs(p-s.p2);
    return getDistanceLP(s, p);
}

double getDistance(Segment s1, Segment s2){
    if(intersect(s1, s2))   return 0.0;
    return min({getDistanceSP(s1, s2.p1), getDistanceSP(s1, s2.p2), 
                getDistanceSP(s2, s1.p1), getDistanceSP(s2, s1.p2)});
}


bool isOrthogonal(Vector a, Vector b){
    return equals(dot(a, b), 0.0);
}
bool isOrthogonal(Point a1, Point a2, Point b1, Point b2){
    return isOrthogonal(a1-a2, b1-b2);
}
bool isOrthogonal(Segment s1, Segment s2){
    return equals(dot(s1.p2-s1.p1, s2.p2-s2.p1), 0.0);
}
bool isParallel(Vector a, Vector b){
    return equals(cross(a, b), 0.0);
}
bool isParallel(Point a1, Point a2, Point b1, Point b2){
    return isParallel(a1-a2, b1-b2);
}
bool isParallel(Segment s1, Segment s2){
    return equals(cross(s1.p2-s1.p1, s2.p2-s2.p1), 0.0);
}


static const int COUNTER_CLOCKWISE = 1;
static const int CLOCKWISE = -1;
static const int ONLINE_BACK = 2;   // p2->p0->p1
static const int ONLINE_FRONT = -2; // p0->p1->p2
static const int ON_SEGMENT = 0;    // p0->p2->p1
int ccw(Point p0, Point p1, Point p2){
    Vector a = p1 - p0;
    Vector b = p2 - p0;
    if(cross(a, b) > EPS)   return COUNTER_CLOCKWISE;
    if(cross(a, b) < -EPS)  return CLOCKWISE;
    if(dot(a, b) < -EPS)    return ONLINE_BACK;
    if(norm(a) < norm(b))   return ONLINE_FRONT;
    return ON_SEGMENT;
}

bool intersect(Point p1, Point p2, Point p3, Point p4){
    return (ccw(p1, p2, p3) * ccw(p1, p2, p4) <= 0 &&
            ccw(p3, p4, p1) * ccw(p3, p4, p2) <= 0);
}
bool intersect(Segment s1, Segment s2){
    return intersect(s1.p1, s1.p2, s2.p1, s2.p2);
}
bool intersect(Circle c, Line l){
    return getDistanceLP(l, c.c) < c.r+EPS;
}
bool intersect(Circle c1, Circle c2){
    return abs(c1.r-c2.r) <= getDistance(c1.c, c2.c) && getDistance(c1.c, c2.c) < c1.r+c2.r+EPS;
}

Point project(Segment s, Point p){
    Vector base = s.p2 - s.p1;
    double r = dot(p - s.p1, base) / norm(base);
    return s.p1 + base * r;
}

Point reflect(Segment s, Point p){
    return p + (project(s, p) - p) * 2.0;
}

Point getCrossPoint(Segment s1, Segment s2){
    Vector base = s2.p2 - s2.p1;
    double d1 = abs(cross(base, s1.p1-s2.p1));
    double d2 = abs(cross(base, s1.p2-s2.p1));
    double t = d1 / (d1 + d2);
    return s1.p1 + (s1.p2 - s1.p1) * t;
}

pair<Point,Point> getCrossPoints(Circle c, Line l){
    assert(intersect(c, l));
    Vector pr = project(l, c.c);
    Vector e = (l.p2 - l.p1) / abs(l.p2 - l.p1);
    double base = sqrt(c.r * c.r - norm(pr - c.c));
    return make_pair(pr + e*base, pr - e*base);
}

pair<Point,Point> getCrossPoints(Circle c1, Circle c2){
    assert(intersect(c1, c2));
    double d = abs(c1.c - c2.c);
    double a = acos( (c1.r*c1.r + d*d - c2.r*c2.r)/(2*c1.r*d) );
    double t = arg(c2.c - c1.c);
    return make_pair(c1.c + polar(c1.r, t+a), c1.c + polar(c1.r, t-a));
}

pair<Point,Point> getContactPoints(Circle c, Point p){
    assert(c.r < getDistance(c.c, p));
    double d = getDistance(c.c, p);
    return getCrossPoints(c, Circle(p, sqrt(d*d-c.r*c.r)));
}

double area(Polygon g){
    if(g.size() < 3)    return 0;
    int n = g.size();
    Point o(0.0, 0.0);
    double s = 0.0;
    for(int i = 0; i < n; i++)  s += cross(g[i]-o, g[(i+1)%n]-o);
    return abs(s) / 2.0;
}

bool isConvex(Polygon g){
    bool ret = true;
    int n = g.size();
    for(int i = 0; i < n; i++){
        for(int j = i+1; j < n; j++){
            if(cross(g[i]-g[(i+n-1)%n], g[j]-g[(i+n-1)%n]) < -EPS || cross(g[(i+1)%n]-g[i], g[j]-g[i]) < -EPS){
                ret = false;
            }
        }
    }
    return ret;
}

static const int IN = 2;
static const int ON = 1;
static const int OUT = 0;
int contains(Polygon g, Point p){
    int n = g.size();
    bool x = false;
    for(int i = 0; i < n; i++){
        Point a = g[i] - p, b = g[(i+1)%n] - p;
        if(abs(cross(a, b)) < EPS && dot(a, b) < EPS)   return ON;
        if(a.y > b.y)   swap(a, b);
        if(a.y < EPS && EPS < b.y && cross(a, b) > EPS) x = !x;
    }
    return x ? IN : OUT;
}


double arg(Vector p){
    return atan2(p.y, p.x);
}

Vector polar(double a, double r){
    return Point(a * cos(r), a * sin(r));
}


Polygon andrewScan(Polygon g){
    Polygon u, l;
    if(g.size() < 3)    return g;
    sort(g.begin(), g.end());
    u.push_back(g[0]);
    u.push_back(g[1]);
    l.push_back(g[g.size()-1]);
    l.push_back(g[g.size()-2]);

    // upper
    for(int i = 2; i < g.size(); i++){
        for(int n = u.size(); n >= 2 && ccw(u[n-2], u[n-1], g[i]) != CLOCKWISE; n--){
            u.pop_back();
        }
        u.push_back(g[i]);
    }

    // lower
    for(int i = g.size()-3; i >= 0; i--){
        for(int n = l.size(); n >= 2 && ccw(l[n-2], l[n-1], g[i]) != CLOCKWISE; n--){
            l.pop_back();
        }
        l.push_back(g[i]);
    }

    reverse(l.begin(), l.end());
    for(int i = u.size()-2; i >= 1; i--)    l.push_back(u[i]);

    return l;
}

double convexDiameter(Polygon g){
    double d = 0.0;
    int n = g.size();
    int is = 0, js = 0;
    for(int i = 1; i < n; i++){
        if(g[i].y > g[is].y)    is = i;
        if(g[i].y < g[js].y)    js = i;
    }
    d = getDistance(g[is], g[js]);

    int i = is, j = js, maxi = is, maxj = js;
    do{
        if(cross(g[(i+1)%n]-g[i], g[(j+1)%n]-g[j]) >= 0.0)  j = (j+1)%n;
        else    i = (i+1)%n;
        if(getDistance(g[i], g[j]) > d){
            d = getDistance(g[i], g[j]);
            maxi = i, maxj = j;
        }
    }while(i != is || j != js);

    return d; // farthest pair is (maxi, maxj).
}


double todeg(double d){
    return d / acos(0.0) / 2 * 180;
}

int main(){
    int n;
    cin >> n;
    vector<Point> vp;
    for(int i = 0; i < n; i++){
        int x, y;
        cin >> x >> y;
        vp.push_back(Point(x, y));
    }
    sort(vp.begin(), vp.end());
    double ans = n*360.0;
    do{
        double tmp = 0;
        Point p = Point(1, 0);
        Point from = Point(0,0);
        for(int i = 0; i < n; i++){
            double way = todeg(arg(vp[i]-from));
            tmp += min(abs(todeg(arg(p))-way), 360-abs(todeg(arg(p))-way));
            p = vp[i]-from;
            from = vp[i];
        }
        double way = todeg(arg(Point(0,0)-vp.back()));
        tmp += min(abs(todeg(arg(p))-way), 360-abs(todeg(arg(p))-way));
        ans = min(ans, tmp);
    }while(next_permutation(vp.begin(), vp.end()));
    cout << fixed << setprecision(12) << ans << endl;
    return 0;
}