UVa 10245

#include <bits/stdc++.h>
// #include <iostream>
// #include <cstdio>
// #include <cstdlib>
// #include <algorithm>
// #include <cmath>
// #include <vector>
// #include <set>
// #include <map>
// #include <queue>
// #include <stack>
// #include <ctime>
// #include <cassert>
// #include <complex>
// #include <string>
// #include <cstring>
// #include <bitset>
using namespace std;

// #pragma GCC optimize("Ofast,no-stack-protector")
// #pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
// #pragma GCC optimize("unroll-loops")

#define ll              long long int
#define vi              vector< int >
#define vll             vector< ll >

#define sc              scanf
#define pf              printf
#define cspf(i)         pf("Case %d:\n", i)
#define spc             pf(" ")
#define line            pf("\n")

#define ff              first
#define ss              second
#define mp              make_pair
#define pb              push_back
#define ppb             pop_back
#define tp(v,j)         get<j>(v)
#define Log(b,x)        (log(x)/log(b))

#define FOR(i,x,y)      for(int i = int(x); i < int(y); i++)
#define ROF(i,x,y)      for(int i = int(x)-1; i >= int(y); i--)
#define clr(arr,x)      memset(arr, x, sizeof arr)
#define vout(v,sz)      for(int w=0;w<sz;w++){if(w) spc; cout<<v[w];}
#define all(v)          v.begin(), v.end()
#define rall(v)         v.rbegin(), v.rend()
#define unq(v)          sort(all(v)),(v).resize(unique(all(v))-v.begin())
#define fastIO          ios::sync_with_stdio(false); cin.tie(nullptr); cout.tie(nullptr)

#define sc1(x)          sc("%d",&x)
#define sc2(x,y)        sc("%d %d", &x, &y)
#define sc3(x,y,z)      sc("%d %d %d", &x, &y, &z)
#define scl1(x)         sc("%lld",&x)
#define scl2(x,y)       sc("%lld %lld", &x, &y)
#define scf1(x)         sc("%lf",&x);
#define scf2(x,y)       sc("%lf %lf", &x, &y)

#define pf1(x)          pf("%d",x)
#define pf2(x,y)        pf("%d %d", x, y)
#define pfl1(x)         pf("%lld\n",x)
#define pfl2(x,y)       pf("%lld %lld", x, y)

#define MAX             1e9
#define MaxN            10000
#define inf             0x3f3f3f3f
#define PI              acos(-1.0)  // 3.1415926535897932
#define eps             1e-9

#ifdef ERFANUL007
    #define debug(...) __f(#__VA_ARGS__, __VA_ARGS__)
    template < typename Arg1 >
    void __f(const char* name, Arg1&& arg1){
        cout << name << " = " << arg1 << std::endl;
    }
    template < typename Arg1, typename... Args>
    void __f(const char* names, Arg1&& arg1, Args&&... args){
        const char* comma = strchr(names, ',');
        cout.write(names, comma - names) << " = " << arg1 <<" | ";
        __f(comma+1, args...);
    }
#else
    #define debug(...)
#endif

template <class T> inline T bigMod(T p,T e,T M){T ret=1; for(;e>0;e>>=1){ if(e&1) ret=(ret*p)%M; p=(p*p)%M;} return (T)ret;}
template <class T> inline T modInverse(T a,T M){return bigMod(a,M-2,M);}
template <class T> inline T gcd(T a,T b){if(b==0)return a;return gcd(b,a%b);}
template <class T> inline T lcm(T a,T b) {a=abs(a);b=abs(b); return (a/gcd(a,b))*b;}

int dx[] = { 1,-1, 0, 0};                //graph moves
int dy[] = { 0, 0, 1,-1};               //graph moves

struct PT{
    double x, y;
    PT(){}
    PT(double x, double y) : x(x), y(y) {}
    void scan(){ scanf("%lf %lf",&x,&y);}
    inline bool operator == (const PT &p) const {
        return (abs(x - p.x) < eps && abs(y - p.y) < eps);
    }
    inline bool operator < (const PT &p) const {
        return (((x + eps) < p.x) || (abs(x - p.x) < eps && (y + eps) < p.y));
    }
};

double SQ(double x){ return x*x;}
/* return the euclidean distance of two point */
double Dis(PT a, PT b){ return SQ(a.x-b.x) + SQ(a.y-b.y);}

double absDis(PT a, PT b){ return sqrt(Dis(a, b));}

/* receive a list of sorted by x point
find the closest distance of any pair of points recursively
O(n(log n)^2) */
vector< PT > v;
double ClosestDistance(int lo, int hi){
    if(lo == hi) return MAX;
    if(lo + 1 == hi) return absDis(v[lo], v[hi]);

    int mid = (lo + hi)/2;
    double val = min( ClosestDistance(lo, mid), ClosestDistance(mid+1, hi));

    vector< PT > strip;
    for(int i=lo; i<=hi; i++){
        if((abs(v[mid].x - v[i].x) + eps) < val){
            strip.pb(v[i]);
        }
    }

    sort(strip.begin(), strip.end(), [](const PT &a, const PT &b) -> bool {
        return (a.y + eps) < b.y;
    }); // sort by y coordinates

    for(int i=0; i<strip.size(); i++){
        for(int j=i+1; j<strip.size() && (abs(strip[i].y - strip[j].y) + eps) < val; j++){
            val = min(val, absDis(strip[i], strip[j]));
        }
    }
    return val;
}


int main()
{
    #ifdef ERFANUL007
        clock_t tStart = clock();
        freopen("input.txt", "r", stdin);
        freopen("output.txt", "w", stdout);
    #endif

    int n;
    while(~sc1(n) && n){
        v.clear();
        for(int i=0; i<n; i++){
            PT a; a.scan();
            v.pb(a);
        }
        sort(all(v));
        double ans = ClosestDistance(0, n-1);
        if(abs(ans - MaxN) < 1e-4 || (MaxN + eps) < ans) pf("INFINITY\n");
        else pf("%.4f\n", ans);
    }

    #ifdef ERFANUL007
        fprintf(stderr, "\n>> Runtime: %.10fs\n", (double) (clock() - tStart) / CLOCKS_PER_SEC);
    #endif

    return 0;
}