Problem: Find the diameter of a convex polygon g. In other words, find a pair of points that have maximum distance between them.

Constraints

* 3 ≤ n ≤ 80000
* -100 ≤ xi, yi ≤ 100
* No point in the g will occur more than once.

Input


n
x1 y1
x2 y2
:
xn yn


The first integer n is the number of points in g.

In the following lines, the coordinate of the i-th point pi is given by two real numbers xi and yi. The coordinates of points are given in the order of counter-clockwise visit of them. Each value is a real number with at most 6 digits after the decimal point.

Output

Print the diameter of g in a line. The output values should be in a decimal fraction with an error less than 0.000001.

Examples

Input

3
0.0 0.0
4.0 0.0
2.0 2.0


Output

4.00


Input

4
0.0 0.0
1.0 0.0
1.0 1.0
0.0 1.0


Output

1.414213562373

Solution (in CPP):

Solution:
#include <complex>
#include <vector>
#include <map>
#include <algorithm>
#include <iostream>
#include <cstdio>
#include <cassert>

using namespace std;

#define REP(i,n) for(int i = 0; i < (int)(n); ++i)
#define FOR(i,a,b) for(int i = (a); i < (int)(b); ++i)
#define ALL(c) (c).begin(), (c).end()
#define SIZE(v) ((int)v.size())

#define pb push_back
#define mp make_pair
#define mt make_tuple

#define curr(P, i) P[(i) % P.size()]
#define next(P, i) P[(i+1) % P.size()]
#define prev(P, i) P[(i+P.size()-1) % P.size()]
#define diff(P, i) (next(P, i) - curr(P, i))

const double EPS = 1e-8;
const double INF = 1e12;

typedef complex<double> P;
struct L : public vector<P> {
    L(const P &a, const P &b) {
        push_back(a); push_back(b);
    }
};
typedef vector<P> Polygon;

namespace std {
    bool operator < (const P& a, const P& b) {
        return real(a) != real(b) ? real(a) < real(b) : imag(a) < imag(b);
    }
}

// ??????
double dot(const P& a, const P& b) {
    return real(conj(a)*b);
}

// ????¬?????????????2??????
double norm(const P& a) {
    return real(conj(a)*a);
}

// ??????
double cross(const P& a, const P& b) {
    return imag(conj(a)*b);
}

// ???p2?????????p0, p1???????????´???????°???±?????????
P projection(const P& p0, const P& p1, const P& p2) {
    // ???????????????????????´???
    P vec1 = p1 - p0;
    P vec2 = p2 - p0;
    return p0 + vec1 * dot(vec1, vec2) / dot(vec1, vec1);
}

// projection?????\??¨???
// not verified
P projection(const L &l, const P &p) {
    double t = dot(p-l[0], l[0]-l[1]) / norm(l[0]-l[1]);
    return l[0] + t*(l[0]-l[1]);
}

// ???p0, p1???????????´??????????§°?????¨????????????p2??¨????§°??????
P reflection(const P& p0, const P& p1, const P& p2) {
    P proj = projection(p0, p1, p2);
    return proj - (p2 - proj);
}

int ccw(P a, P b, P c) {
    b -= a; c -= a;
    if (cross(b, c) > 0)   return +1;       // counter clockwise
    if (cross(b, c) < 0)   return -1;       // clockwise
    if (dot(b, c) < 0)     return +2;       // c--a--b on line
    if (norm(b) < norm(c)) return -2;       // a--b--c on line
    return 0;                               // a--c--b on line
}

// 2??´?????????????????????
bool is_parallel(const L& l1, const L& l2) {
    P p1 = l1[1] - l1[0];
    P p2 = l2[1] - l2[0];
    auto res = ccw(p1, p2, P(0,0));
    return (res == 2 || res == -2 || res == 0);
}

// 2??´???????????´?????????
bool is_ortho(const L& l1, const L& l2) {
    P p1 = l1[1] - l1[0];
    P p2 = l2[1] - l2[0];
    return dot(p1, p2) == 0;
}

// l: line(??´???)
// s: segment(??????)
// not verified
bool intersectLL(const L &l, const L &m) {
  return abs(cross(l[1]-l[0], m[1]-m[0])) > EPS || // non-parallel
         abs(cross(l[1]-l[0], m[0]-l[0])) < EPS;   // same line
}

// not verified
bool intersectLS(const L &l, const L &s) {
    return cross(l[1]-l[0], s[0]-l[0])*       // s[0] is left of l
        cross(l[1]-l[0], s[1]-l[0]) < EPS; // s[1] is right of l
}

// not verified
bool intersectLP(const L &l, const P &p) {
    return abs(cross(l[1]-p, l[0]-p)) < EPS;
}

bool intersectSS(const L &s, const L &t) {
    return ccw(s[0],s[1],t[0])*ccw(s[0],s[1],t[1]) <= 0 &&
        ccw(t[0],t[1],s[0])*ccw(t[0],t[1],s[1]) <= 0;
}

// not verified
bool intersectSP(const L &s, const P &p) {
    return abs(s[0]-p)+abs(s[1]-p)-abs(s[1]-s[0]) < EPS; // triangle inequality
}

// not verified
double distanceLP(const L &l, const P &p) {
    return abs(p - projection(l, p));
}

// not verified
double distanceLL(const L &l, const L &m) {
    return intersectLL(l, m) ? 0 : distanceLP(l, m[0]);
}

// not verified
double distanceLS(const L &l, const L &s) {
    if (intersectLS(l, s)) return 0;
    return min(distanceLP(l, s[0]), distanceLP(l, s[1]));
}

double distanceSP(const L &s, const P &p) {
    const P r = projection(s, p);
    if (intersectSP(s, r)) return abs(r - p);
    return min(abs(s[0] - p), abs(s[1] - p));
}

double distanceSS(const L &s, const L &t) {
    if (intersectSS(s, t)) return 0;
    return min(min(distanceSP(s, t[0]), distanceSP(s, t[1])),
               min(distanceSP(t, s[0]), distanceSP(t, s[1])));
}

// 2??´????????????
P crosspoint(const L &l, const L &m) {
    double A = cross(l[1] - l[0], m[1] - m[0]);
    double B = cross(l[1] - l[0], l[1] - m[0]);
    if (abs(A) < EPS && abs(B) < EPS) return m[0]; // same line
    if (abs(A) < EPS) assert(false); // !!!PRECONDITION NOT SATISFIED!!!
    return m[0] + B / A * (m[1] - m[0]);
}

// ????§???¢?????¢???????±???????
// P???????????¨???????????????
double area(const Polygon& poly) {
    double area = 0.0;
    REP(i, SIZE(poly))
        area += cross(curr(poly, i), next(poly, i));
    return abs(area) * 0.5;
}

// ??????????±??????????????????????????????????????????????
// ????????????????¨?????????§????????????
// not verified
Polygon convexHull(const Polygon& poly) {
    Polygon ps = poly;

    int n = ps.size(), k = 0;
    sort(ALL(ps));
    Polygon ch(2*n);
    for (int i = 0; i < n; ch[k++] = ps[i++]) // lower-hull
        while (k >= 2 && ccw(ch[k-2], ch[k-1], ps[i]) <= 0) --k;
    for (int i = n-2, t = k+1; i >= 0; ch[k++] = ps[i--]) // upper-hull
        while (k >= t && ccw(ch[k-2], ch[k-1], ps[i]) <= 0) --k;
    ch.resize(k-1);
    return ch;
}

// ??????????±????????????????????????????????????????????????????
// ????????????????¨?????????§????????????
// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_4_A&lang=jp
Polygon convexHullInludingPointsOnEdge(const Polygon& poly) {
    Polygon ps = poly;

    int n = ps.size(), k = 0;
    sort(ALL(ps));
    Polygon ch(2*n);
    for (int i = 0; i < n; ch[k++] = ps[i++]) // lower-hull
        while (k >= 2 && ccw(ch[k-2], ch[k-1], ps[i]) == -1) --k;
    for (int i = n-2, t = k+1; i >= 0; ch[k++] = ps[i--]) // upper-hull
        while (k >= t && ccw(ch[k-2], ch[k-1], ps[i]) == -1) --k;
    ch.resize(k-1);
    return ch;
}

// ?????§??????
// poly?????????????¨???¨?????§?????????????´?????????????????????¨???????????????
// ???????????´??????????????¶???????¨±???
bool isConvex(const Polygon &poly) {
    REP(i, SIZE(poly)) {
        if (ccw(prev(poly, i), curr(poly, i), next(poly, i)) == -1)
            return false;
    }
    return true;
}

// poly????????§???????????¨?????????
// 0: OUT
// 1: ON
// 2: IN
// not verified
enum { OUT, ON, IN };
int convexContains(const Polygon &poly, const P &p) {
    const int n = poly.size();
    P g = (poly[0] + poly[n/3] + poly[2*n/3]) / 3.0; // inner-P
    int a = 0, b = n;
    while (a+1 < b) { // invariant: c is in fan g-poly[a]-poly[b]
        int c = (a + b) / 2;
        if (cross(poly[a]-g, poly[c]-g) > 0) { // angle < 180 deg
            if (cross(poly[a]-g, p-g) > 0 && cross(poly[c]-g, p-g) < 0) b = c;
            else                                                  a = c;
        } else {
            if (cross(poly[a]-g, p-g) < 0 && cross(poly[c]-g, p-g) > 0) a = c;
            else                                                  b = c;
        }
    }
    b %= n;
    if (cross(poly[a] - p, poly[b] - p) < 0) return OUT;
    if (cross(poly[a] - p, poly[b] - p) > 0) return IN;
    return ON;
}

// poly????????§???????????????
// 0: OUT
// 1: ON
// 2: IN
int contains(const Polygon& poly, const P& p) {
    bool in = false;
    REP(i, SIZE(poly)) {
        P a = curr(poly,i) - p, b = next(poly,i) - p;
        if (imag(a) > imag(b)) swap(a, b);
        if (imag(a) <= 0 && 0 < imag(b))
            if (cross(a, b) < 0) in = !in;
        if (cross(a, b) == 0 && dot(a, b) <= 0) return ON;
    }
    return in ? IN : OUT;
}


// ????§???¢?????´?????????2???????????????
// ??\????????????????????§?????????????????????
double convexDiameterSquared(const Polygon &poly) {
    const int n = poly.size();
    int is = 0, js = 0;
    for (int i = 1; i < n; ++i) {
        if (imag(poly[i]) > imag(poly[is])) is = i;
        if (imag(poly[i]) < imag(poly[js])) js = i;
    }
    double maxd = norm(poly[is]-poly[js]);

    int i, maxi, j, maxj;
    i = maxi = is;
    j = maxj = js;
    do {
        if (cross(diff(poly,i), diff(poly,j)) >= 0) j = (j+1) % n;
        else i = (i+1) % n;
        if (norm(poly[i]-poly[j]) > maxd) {
            maxd = norm(poly[i]-poly[j]);
            maxi = i; maxj = j;
        }
    } while (i != is || j != js);
    return maxd; /* farthest pair is (maxi, maxj). */
}

int main(){
    int N;
    cin >> N;
    Polygon poly;
    REP(n, N) {
        double x, y;
        cin >> x >> y;
        poly.pb( P(x,y) );
    }

    printf("%.10lf\n", sqrt(convexDiameterSquared(poly)));

    return 0;
}