#include<bits/stdc++.h>
using namespace std;

typedef long long int ll;
typedef pair<int, int> pii;
typedef vector<int> vi;
typedef vector<pair<int, int> > vii;
#define rrep(i, m, n) for(int (i)=(m); (i)<(n);  (i)++)
#define erep(i, m, n) for(int (i)=(m); (i)<=(n); (i)++)
#define  rep(i, n)    for(int (i)=0; (i)<(n);  (i)++)
#define rrev(i, m, n) for(int (i)=(n)-1; (i)>=(m); (i)--)
#define erev(i, m, n) for(int (i)=(n); (i)>=(m); (i)--)
#define  rev(i, n)    for(int (i)=(n)-1; (i)>=0; (i)--)
#define vrep(i, c)    for(__typeof((c).begin())i=(c).begin(); i!=(c).end(); i++)
#define  ALL(v)       (v).begin(), (v).end()
#define pb            push_back
#define mp            make_pair
template<class T, class S> inline bool minup(T& m, const S x){ return m>(T)x ? (m=(T)x, true) : false; }
template<class T, class S> inline bool maxup(T& m, const S x){ return m<(T)x ? (m=(T)x, true) : false; }

static const int    INF = 1000000000;
static const ll     MOD = 1000000007LL;
static const double EPS = 1E-8;

template<typename T> T add(T x, T y){ if(abs(x+y) < EPS*(abs(x)+abs(y))) return 0; return x + y; }
template<typename T> inline bool semieq(T x, T y){ return abs(x - y) < EPS; }
template<typename T> inline bool semige(T x, T y){ return y - x < -EPS; }
template<typename T> inline bool semile(T x, T y){ return x - y < -EPS; }


struct Point : public complex<double>
{
public:
  Point(const double x = 0.0, const double y = 0.0) { this->real(x);  this->imag(y); }
  Point(const complex<double> w)  { this->real(w.real());  this->imag(w.imag()); }
  inline double dot(Point p){ return (conj(*this) * p).real(); }  // ??????
  inline double det(Point p){ return (conj(*this) * p).imag(); }  // ??????
};

namespace std
{
  inline bool operator < (const Point& a, const Point& b)
  {
    return real(a) != real(b) ? real(a) < real(b) : imag(a) < imag(b);
  }
}
typedef vector<Point> Polygon;
inline Point currPoint(vector<Point> P, int i){ return P[i]; }
inline Point nextPoint(vector<Point> P, int i){ return P[(i+1)%P.size()]; }
inline Point diffPoint(vector<Point> P, int i){ return nextPoint(P, i) - currPoint(P, i); }


int ccw(Point a, Point b, Point c)
{
  b -= a;
  c -= a;
  if(b.det(c) > 0.0)    return  1;         // counter clockwise
  if(b.det(c) < 0.0)    return -1;         // clockwise
  if(b.dot(c) < 0.0)    return  2;         // c--a--b on line
  if(norm(b) < norm(c)) return -2;         // a--b--c on line
  return 0;
}


struct Circle : Point
{
private:
  Point p;
  double r;

public:
  Circle() : p(Point(0.0, 0.0)), r(0.0) {}
  Circle(Point p, double r) : p(p), r(r) {}
  Circle(double x, double y, double r) : p(Point(x, y)), r(r) {}
  inline Point center(){ return this->p; }
  inline double radius(){ return this->r; }
};


vector<Point> intersectionOfCC(Circle A, Circle B)
{
  vector<Point> ret(2);
  double x1 = A.center().real(), y1 = A.center().imag(), r1 = A.radius();
  double x2 = B.center().real(), y2 = B.center().imag(), r2 = B.radius();
  double dx = x2 - x1;
  double dy = y2 - y1;
  double a = dx * dx + dy * dy;
  double b = ((r1 * r1 - r2 * r2) / a + 1) / 2;
  double d = r1 * r1 / a - b * b;
  double x3 = x1 + dx * b;
  double y3 = y1 + dy * b;
  double x4 = -dy * sqrt(d);
  double y4 =  dx * sqrt(d);
  ret[0] = Point(x3 - x4, y3 - y4);
  ret[1] = Point(x3 + x4, y3 + y4);
  return ret;
}


int N;
double X, R;
Circle* C;

bool check(double d)
{
  deque<int> deq;
  int pos = 0;
  deq.pb(pos++);
  while(!deq.empty()){
    int f = deq.front();
    Point c = C[f].center();
    double hx = c.real();
    double hr = C[f].radius();
    if(semile(hr, d / 2.0)){
      deq.pop_front();
      if(pos < N) deq.pb(pos++);
      continue;
    }
    double x = hx - sqrt(hr * hr - d * d / 4.0);
    Point np = Point(x + d, d / 2.0);
    if(!semige(abs(c - np), hr)) return true;
    int sz = deq.size();
    int t1 = deq.at(sz - 1);
    if(sz > 1){
      int t2 = deq.at(sz - 2);
      vector<Point> in = intersectionOfCC(C[t1], C[t2]);
      double y = max(in[0].imag(), in[1].imag());
      if(!semige(abs(C[t1].center() - np), C[t1].radius()))
        if(!semige(d / 2.0, y)) return true;
      if(semile(y, d / 2.0)){
        deq.pop_front();
        continue;
      }
    }
    if(pos >= N) deq.pop_front();
    if(pos < N) deq.pb(pos++);
  }
  return false;
}

int main(int argc, char *argv[])
{
  while(cin >> N, N){
    C = new Circle[N];
    double l = 0.0;
    double r = INF;
    rep(i, N){
      cin >> X >> R;
      C[i] = Circle(X, 0.0, R);
      maxup(l, R);
    }

    rep(_, 50){
      double mid = (l + r) / 2.0;
      if(check(mid)) l = mid;
      else r = mid;
    }

    printf("%.15f\n", r);
    
    delete[] C;
  }
  
  return 0;
}

Measured memory_bytes: 3440