Problem: The main land of Japan called Honshu is an island surrounded by the sea. In such an island, it is natural to ask a question: "Where is the most distant point from the sea?" The answer to this question for Honshu was found in 1996. The most distant point is located in former Usuda Town, Nagano Prefecture, whose distance from the sea is 114.86 km.

In this problem, you are asked to write a program which, given a map of an island, finds the most distant point from the sea in the island, and reports its distance from the sea. In order to simplify the problem, we only consider maps representable by convex polygons.



Input

The input consists of multiple datasets. Each dataset represents a map of an island, which is a convex polygon. The format of a dataset is as follows.


n
x1    y1
.
.
.
xn    yn


Every input item in a dataset is a non-negative integer. Two input items in a line are separated by a space.

n in the first line is the number of vertices of the polygon, satisfying 3 ≤ n ≤ 100. Subsequent n lines are the x- and y-coordinates of the n vertices. Line segments (xi, yi) - (xi+1, yi+1) (1 ≤ i ≤ n - 1) and the line segment (xn, yn) - (x1, y1) form the border of the polygon in counterclockwise order. That is, these line segments see the inside of the polygon in the left of their directions. All coordinate values are between 0 and 10000, inclusive.

You can assume that the polygon is simple, that is, its border never crosses or touches itself. As stated above, the given polygon is always a convex one.

The last dataset is followed by a line containing a single zero.

Output

For each dataset in the input, one line containing the distance of the most distant point from the sea should be output. An output line should not contain extra characters such as spaces.

The answer should not have an error greater than 0.00001 (10-5 ). You may output any number of digits after the decimal point, provided that the above accuracy condition is satisfied.

Example

Input

4
0 0
10000 0
10000 10000
0 10000
3
0 0
10000 0
7000 1000
6
0 40
100 20
250 40
250 70
100 90
0 70
3
0 0
10000 10000
5000 5001
0


Output

5000.000000
494.233641
34.542948
0.353553

Solution (in CPP):

Solution:
#include <vector>
#include <iostream>
#include <utility>
#include <algorithm>
#include <string>
#include <deque>
#include <queue>
#include <tuple>
#include <queue>
#include <functional>
#include <cmath>
#include <iomanip>
#include <map>
#include <set>
#include <numeric>
#include <unordered_map>
#include <unordered_set>
#include <complex>
#include <iterator>
#include <array>
#include <memory>
#include <random>
//cin.sync_with_stdio(false);
//streambuf
using namespace std;
typedef long long ll;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef pair<double, double> pdd;
using vi = vector<int>;
using vll = vector<ll>;
using vpii = vector<pii>;
using vpll = vector<pll>;
using ti3 = tuple<int, int, int>;
using vti3 = vector<ti3>;
template<class T, int s>using va = vector<array<T, s>>;
template<class T, class T2> using umap = unordered_map<T, T2>;
template<class T> using uset = unordered_set<T>;
template<class T, class S> void cmin(T &a, const S &b) { if (a > b)a = b; }
template<class T, class S> void cmax(T &a, const S &b) { if (a < b)a = b; }
#define ALL(a) a.begin(),a.end()
#define rep(i,a) for(int i=0;i<a;i++)
#define rep1(i,a) for(int i=1;i<=a;i++)
#define rrep(i,a) for(int i=(a)-1;i>=0;i--)
#define rrep1(i,a) for(int i=a;i;i--)
const ll mod = 1000000007;
#define REP rep
template<class T>using heap = priority_queue<T, vector<T>, greater<T>>;
template<class T>using pque = priority_queue<T, vector<T>, function<T(T, T)>>;
template <class T>
inline void hash_combine(size_t & seed, const T & v) {
	hash<T> hasher;
	seed ^= hasher(v) + 0x9e3779b9 + (seed << 6) + (seed >> 2);
}
namespace std {
	template<typename S, typename T> struct hash<pair<S, T>> {
		inline size_t operator()(const pair<S, T> & v) const {
			size_t seed = 0;
			hash_combine(seed, v.first);
			hash_combine(seed, v.second);
			return seed;
		}
	};
	// Recursive template code derived from Matthieu M.
	template <class Tuple, size_t Index = std::tuple_size<Tuple>::value - 1>
	struct HashValueImpl {
		static void apply(size_t& seed, Tuple const& tuple) {
			HashValueImpl<Tuple, Index - 1>::apply(seed, tuple);
			hash_combine(seed, std::get<Index>(tuple));
		}
	};
	template <class Tuple>
	struct HashValueImpl<Tuple, 0> {
		static void apply(size_t& seed, Tuple const& tuple) {
			hash_combine(seed, std::get<0>(tuple));
		}
	};
	template <typename ... TT>
	struct hash<std::tuple<TT...>> {
		size_t operator()(std::tuple<TT...> const& tt) const {
			size_t seed = 0;
			HashValueImpl<std::tuple<TT...> >::apply(seed, tt);
			return seed;
		}
	};
}
template<class T>int id(vector<T> &a, T b) {
	return lower_bound(ALL(a), b) - a.begin();
}
ll pow(ll base, ll i, ll mod) {
	ll a = 1;
	while (i) {
		if (i & 1) {
			a *= base;
			a %= mod;
		}
		base *= base;
		base %= mod;
		i /= 2;
	}
	return a;
}
ll gcd(ll a, ll b) {
	while (b) {
		ll c = a%b;
		a = b;
		b = c;
	}
	return a;
}
ll lcm(ll a, ll b) {
	return a / gcd(a, b)*b;
}
int popcnt(unsigned long long a) {
	a = (a & 0x5555555555555555) + (a >> 1 & 0x5555555555555555);
	a = (a & 0x3333333333333333) + (a >> 2 & 0x3333333333333333);
	a = (a & 0x0f0f0f0f0f0f0f0f) + (a >> 4 & 0x0f0f0f0f0f0f0f0f);
	a = (a & 0x00ff00ff00ff00ff) + (a >> 8 & 0x00ff00ff00ff00ff);
	a = (a & 0x0000ffff0000ffff) + (a >> 16 & 0x0000ffff0000ffff);
	return (a & 0xffffffff) + (a >> 32);
}
class unionfind {
	vector<int> par, rank, size_;//????????§??????????????¢???????????????????????????rank???????????????size?????????
public:
	unionfind(int n) :par(n), rank(n), size_(n, 1) {
		iota(ALL(par), 0);
	}
	int find(int x) {
		if (par[x] == x)return x;
		return par[x] = find(par[x]);
	}
	void unite(int x, int y) {
		x = find(x), y = find(y);
		if (x == y)return;
		if (rank[x] < rank[y])swap(x, y);
		par[y] = x;
		size_[x] += size_[y];
		if (rank[x] == rank[y])rank[x]++;
	}
	bool same(int x, int y) {
		return find(x) == find(y);
	}
	int size(int x) {
		return size_[find(x)];
	}
};
template<class T, class Func = function<T(T, T)>>
class segtree {
	vector<T> obj;
	int offset;
	Func updater;
	T e;
	int bufsize(int num) {
		int i = 1;
		for (; num >i; i <<= 1);
		offset = i - 1;
		return (i << 1) - 1;
	}
	T query(int a, int b, int k, int l, int r) {
		if (r <= a || b <= l)return e;
		if (a <= l && r <= b)return obj[k];
		else return updater(query(a, b, k * 2 + 1, l, (l + r) / 2), query(a, b, k * 2 + 2, (l + r) / 2, r));
	}
	/*
	template<class QF = function<T(T, T)>>
	auto query(int a, int b, int k, int l, int r,QF qf) {
	if (r <= a || b <= l)return e;
	if (a <= l && r <= b)return obj[k];
	else return qf(query(a, b, k * 2 + 1, l, (l + r) / 2, qf), query(a, b, k * 2 + 2, (l + r) / 2, r, qf));
	}*/
public:
	T query(int a, int b) {//[a,b)
		return query(a, b, 0, 0, offset + 1);
	}/*
	 template<class QF = function<T(T, T)>>
	 auto query(int a, int b,QF &&qf) {//[a,b)
	 return query(a, b, 0, 0, offset + 1,qf);
	 }*/
	void updateall(int l = 0, int r = -1) {
		if (r < 0)r = offset + 1;
		l += offset, r += offset;
		do {
			l = l - 1 >> 1, r = r - 1 >> 1;
			for (int i = l; i < r; i++)obj[i] = updater(obj[i * 2 + 1], obj[i * 2 + 2]);
		} while (l);
	}
	void update(int k, T &a) {
		k += offset;
		obj[k] = a;
		while (k) {
			k = k - 1 >> 1;
			obj[k] = updater(obj[k * 2 + 1], obj[k * 2 + 2]);
		}
	}
	segtree(int n, T e, const Func &updater = Func()) :obj(bufsize(n), e), e(e), updater(updater) {}
	segtree(vector<T> &vec, T e, const Func &updater = Func()) :obj(bufsize(vec.size()), e), e(e), updater(updater) {
		copy(vec.begin(), vec.end(), obj.begin() + offset);
		updateall();
	}
	typename vector<T>::reference operator[](int n) {
		return obj[n + offset];
	}
};
template<class T = int>
class BIT {//????¬????BIT????????????????????????????????°??????????????????
	vector<T> bit;
	int n;
public:
	BIT(int n) :bit(n + 1, 0) {}
	void add(int i, T x) {
		i++;
		while (i <= n) {
			bit[i] += x;
			i += i&-i;
		}
	}
	T sum(int i) {
		T s = 0;
		i++;
		while (i) {
			s += bit[i];
			i &= i - 1;
		}
		return s;
	}
};
template<class T = int>
class rangeadd {
	BIT<T> b0, b1;
public:
	rangeadd(int n) :b0(n), b1(n) {};
	void add(int l, int r, T x) {//[l,r)
		b0.add(l, -x*(l - 1));
		b1.add(l, x);
		b0.add(r, x*r);
		b1.add(r, -x);
	}
	T sum(int i) {
		if (i < 0)return 0;
		return b0.sum(i) + b1.sum(i)*i;
	}
	T sum(int l, int r) {
		return sum(r - 1) - sum(l - 1);
	}
};
typedef complex<ld> P;
typedef vector<P> VP;
const ld eps = 1e-11, pi = acos(-1.0);

ld dot(P a, P b) { return real(conj(a) * b); }
ld cross(P a, P b) { return imag(conj(a) * b); }

namespace std {
	bool operator<(const P &a, const P &b) {
		return abs(a.real() - b.real()) < eps ? a.imag() < b.imag() : a.real() < b.real();
	}
}

struct L { P a, b; };//line->l,segment->s
struct C { P p; ld r; };

int ccw(P a, P b, P c) {
	b -= a; c -= a;
	if (cross(b, c) > eps) return 1;   // counter clockwise
	if (cross(b, c) < -eps) 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
}

bool isis_ll(L l, L m) {//is intersect
	return abs(cross(l.b - l.a, m.b - m.a)) > eps;
}

bool isis_ls(L l, L s) {
	ld a = cross(l.b - l.a, s.a - l.a);
	ld b = cross(l.b - l.a, s.b - l.a);
	return (a * b < eps);
}

bool isis_lp(L l, P p) {
	return abs(cross(l.b - p, l.a - p)) < eps;
}

bool isis_ss(L s, L t) {
	return ccw(s.a, s.b, t.a) * ccw(s.a, s.b, t.b) <= 0 &&
		ccw(t.a, t.b, s.a) * ccw(t.a, t.b, s.b) <= 0;
}

P is_ll(L s, L t) { //intersect
	P sv = s.b - s.a, tv = t.b - t.a;
	return s.a + sv * cross(tv, t.a - s.a) / cross(tv, sv);
}

bool isis_sp(L s, P p) {
	return abs(s.a - p) + abs(s.b - p) - abs(s.b - s.a) < eps;
}

P proj(L l, P p) {
	ld t = dot(p - l.a, l.a - l.b) / norm(l.a - l.b);
	return l.a + t * (l.a - l.b);
}

ld dist_lp(L l, P p) {
	return abs(p - proj(l, p));
}

ld dist_ll(L l, L m) {
	return isis_ll(l, m) ? 0 : dist_lp(l, m.a);
}

ld dist_ls(L l, L s) {
	if (isis_ls(l, s)) return 0;
	return min(dist_lp(l, s.a), dist_lp(l, s.b));
}

ld dist_sp(L s, P p) {
	P r = proj(s, p);
	if (isis_sp(s, r)) return abs(r - p);
	return min(abs(s.a - p), abs(s.b - p));
}

ld dist_ss(L s, L t) {
	if (isis_ss(s, t)) return 0;
	ld a = min(dist_sp(s, t.a), dist_sp(t, s.a));
	ld b = min(dist_sp(s, t.b), dist_sp(t, s.b));
	return min(a, b);
}

VP is_cc(C c1, C c2) {
	VP res;
	ld d = abs(c1.p - c2.p);
	ld rc = (d * d + c1.r * c1.r - c2.r * c2.r) / (2 * d);
	ld dfr = c1.r * c1.r - rc * rc;
	if (abs(dfr) < eps) dfr = 0.0;
	else if (dfr < 0.0) return res; // no intersection
	ld rs = sqrt(dfr);
	P diff = (c2.p - c1.p) / d;
	res.push_back(c1.p + diff * P(rc, rs));
	if (dfr != 0.0) res.push_back(c1.p + diff * P(rc, -rs));
	return res;
}

bool isis_vc(vector<C> vc) {
	VP crs;
	int n = vc.size();
	rep(i, n)rep(j, i)
		for (P p : is_cc(vc[i], vc[j]))
			crs.push_back(p);
	rep(i, n)
		crs.push_back(vc[i].p);
	for (P p : crs) {
		bool valid = true;
		rep(i, n)
			if (abs(p - vc[i].p)>vc[i].r + eps)
				valid = false;
		if (valid) return true;
	}
	return false;
}

VP is_lc(C c, L l) {
	VP res;
	ld d = dist_lp(l, c.p);
	if (d < c.r + eps) {
		ld len = (d > c.r) ? 0.0 : sqrt(c.r * c.r - d * d); //safety;
		P nor = (l.a - l.b) / abs(l.a - l.b);
		res.push_back(proj(l, c.p) + len * nor);
		res.push_back(proj(l, c.p) - len * nor);
	}
	return res;
}

VP is_sc(C c, L l) {
	VP v = is_lc(c, l), res;
	for (P p : v)
		if (isis_sp(l, p)) res.push_back(p);
	return res;
}

vector<L> tangent_cp(C c, P p) {//????????\????
	vector<L> ret;
	P v = c.p - p;
	ld d = abs(v);
	ld l = sqrt(norm(v) - c.r * c.r);
	if (isnan(l)) { return ret; }
	P v1 = v * P(l / d, c.r / d);
	P v2 = v * P(l / d, -c.r / d);
	ret.push_back(L{ p, p + v1 });
	if (l < eps) return ret;
	ret.push_back(L{ p, p + v2 });
	return ret;
}

vector<L> tangent_cc(C c1, C c2) {
	vector<L> ret;
	if (abs(c1.p - c2.p) - (c1.r + c2.r) > -eps) {
		P center = (c1.p * c2.r + c2.p * c1.r) / (c1.r + c2.r);
		ret = tangent_cp(c1, center);
	}
	if (abs(c1.r - c2.r) > eps) {
		P out = (-c1.p * c2.r + c2.p * c1.r) / (c1.r - c2.r);
		vector<L> nret = tangent_cp(c1, out);
		ret.insert(ret.end(), ALL(nret));
	}
	else {
		P v = c2.p - c1.p;
		v /= abs(v);
		P q1 = c1.p + v * P(0, 1) * c1.r;
		P q2 = c1.p + v * P(0, -1) * c1.r;
		ret.push_back(L{ q1, q1 + v });
		ret.push_back(L{ q2, q2 + v });
	}
	return ret;
}

ld area(const VP &p) {//??¢?????
	ld res = 0;
	int n = p.size();
	rep(j, n) res += cross(p[j], p[(j + 1) % n]);
	return res / 2;
}

bool is_polygon(L l, VP &g) {
	int n = g.size();
	for (int i = 0; i < n; i++) {
		P a = g[i];
		P b = g[(i + 1) % n];
		if (isis_ss(l, L{ a, b })) return true;
	}
	return false;
}

int is_in_Polygon(const VP &g, P p) {
	bool in = false;
	int n = g.size();
	for (int i = 0; i < n; i++) {
		P a = g[i] - p, b = g[(i + 1) % n] - p;
		if (imag(a) > imag(b)) swap(a, b);
		if (imag(a) <= 0 && 0 < imag(b))
			if (cross(a, b) < 0) in = !in;
		if (abs(cross(a, b)) < eps && dot(a, b) < eps) return 0; // on
	}
	if (in) return 1; // in
	return -1; // out
}

VP ConvexHull(VP ps) {
	int n = ps.size();
	int k = 0;
	sort(ps.begin(), ps.end());
	VP ch(2 * n);
	for (int i = 0; i < n; ch[k++] = ps[i++])
		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--])
		while (k >= t && ccw(ch[k - 2], ch[k - 1], ps[i]) <= 0) --k;
	ch.resize(k - 1);
	return ch;
}

VP ConvexCut(const VP &ps, L l) {
	VP Q;
	for (int i = 0; i < (int)ps.size(); i++) {
		P A = ps[i], B = ps[(i + 1) % ps.size()];
		if (ccw(l.a, l.b, A) != -1) Q.push_back(A);
		if (ccw(l.a, l.b, A) * ccw(l.a, l.b, B) < 0)
			Q.push_back(is_ll(L{ A, B }, l));
	}
	return Q;
}
class Flow {
	int V;
	struct edge { int to, cap, rev, cost; };
	vector<vector<edge>> G;
	vector<int> level, iter, h, dist, prevv, preve;
public:
	Flow(int size) :G(size + 1), V(size + 1) {
	}
	void add_edge(int from, int to, int cap, int cost = 0) {
		G[from].push_back(edge{ to, cap, (int)G[to].size(),cost });
		G[to].push_back(edge{ from,0,(int)G[from].size() - 1,-cost });
	}
	void bfs(int s) {
		fill(level.begin(), level.end(), -1);
		queue<int> que;
		level[s] = 0;
		que.push(s);
		while (!que.empty()) {
			int v = que.front(); que.pop();
			for (int i = 0; i < G[v].size(); i++) {
				edge &e = G[v][i];
				if (e.cap > 0 && level[e.to] < 0) {
					level[e.to] = level[v] + 1;
					que.push(e.to);
				}
			}
		}
	}
	int dfs(int v, int t, int f) {
		if (v == t)return f;
		for (int &i = iter[v]; i < G[v].size(); i++) {
			edge &e = G[v][i];
			if (e.cap > 0 && level[v] < level[e.to]) {
				int d = dfs(e.to, t, min(f, e.cap));
				if (d > 0) {
					e.cap -= d;
					G[e.to][e.rev].cap += d;
					return d;
				}
			}
		}
		return 0;
	}
	int max_flow(int s, int t) {
		level.resize(V);
		iter.resize(V);
		int flow = 0;
		for (;;) {
			bfs(s);
			if (level[t] < 0)return flow;
			fill(iter.begin(), iter.end(), 0);
			int f;
			while ((f = dfs(s, t, numeric_limits<int>::max()))>0) {
				flow += f;
			}
		}
	}
	typedef pair<int, int> P;
	int min_cost_flow(int s, int t, int f) {
		int res = 0;
		h.resize(V);
		dist.resize(V);
		prevv.resize(V);
		preve.resize(V);
		fill(h.begin(), h.end(), 0);
		while (f > 0) {
			priority_queue<P, vector<P>, greater<P>> que;
			fill(dist.begin(), dist.end(), numeric_limits<int>::max());
			dist[s] = 0;
			que.push({ 0,s });
			while (!que.empty()) {
				P p = que.top(); que.pop();
				int v = p.second;
				if (dist[v] < p.first)continue;
				for (int i = 0; i < G[v].size(); i++) {
					edge &e = G[v][i];
					if (e.cap > 0 && dist[e.to]>dist[v] + e.cost + h[v] - h[e.to]) {
						dist[e.to] = dist[v] + e.cost + h[v] - h[e.to];
						prevv[e.to] = v;
						preve[e.to] = i;
						que.push({ dist[e.to],e.to });
					}
				}
			}
			if (dist[t] == numeric_limits<int>::max()) {
				return -1;
			}
			for (int v = 0; v < V; v++)h[v] += dist[v];

			int d = f;
			for (int v = t; v != s; v = prevv[v]) {
				d = min(d, G[prevv[v]][preve[v]].cap);
			}
			f -= d;
			res += d*h[t];
			for (int v = t; v != s; v = prevv[v]) {
				edge &e = G[prevv[v]][preve[v]];
				e.cap -= d;
				G[v][e.rev].cap += d;
			}
		}
		return res;
	}
};
//end of lib
int main() {
	int n;
	while (cin >> n, n) {
		VP p(n);
		rep(i, n) {
			double x, y;
			cin >> x >> y;
			p[i] = { x,y };
		}
		double ans = 1e9;
		vector<L> l(n);
		rep(i, n)l[i] = { p[i],p[(i + 1) % n] };
		rep(i, n)rep(j, i)rep(k, j) {
			P a = is_ll(l[i], l[j]), b = is_ll(l[j], l[k]), c = is_ll(l[k], l[i]);
			if (ccw(a, b, c) != 0 && ccw(a, b, c) != ccw(l[i].a, l[j].a, l[k].a))continue;
			double t1 = atan2((l[i].a - l[i].b).imag(), (l[i].a - l[i].b).real()), t2 = atan2((l[j].a - l[j].b).imag(), (l[j].a - l[j].b).real()), t3 = atan2((l[k].a - l[k].b).imag(), (l[k].a - l[k].b).real());
			t2 = (t1 + t2) / 2;
			t3 = (t1 + t3) / 2;
			L l1 = (isis_ls(L{ a,a + 1e5l*P(cos(t2),sin(t2)) }, L{ b,c })) ? L{ a,a + 1e5l*P(cos(t2),sin(t2)) } : L{ a,a + 1e5l*P(-sin(t2),cos(t2)) };
			L l2 = (isis_ls(L{ c,c + 1e5l*P(cos(t3),sin(t3)) }, L{ a,b })) ? L{ c,c + 1e5l*P(cos(t3),sin(t3)) } : L{ c,c + 1e5l*P(-sin(t3),cos(t3)) };
			cmin(ans, dist_lp(l[i], is_ll(l1, l2)));
		}
		cout << fixed << setprecision(10) << ans << endl;
	}
}