#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#define ll long long
#define ld long double
#define ull unsigned long long
#define ff first
#define ss second
#define pii pair<int,int>
#define pll pair<long long, long long>
#define vi vector<int>
#define vl vector<long long>
#define pb push_back
#define rep(i, b) for(int i = 0; i < (b); ++i)
#define rep2(i,a,b) for(int i = a; i <= (b); ++i)
#define rep3(i,a,b,c) for(int i = a; i <= (b); i+=c)
#define count_bits(x) __builtin_popcountll((x))
#define all(x) (x).begin(),(x).end()
#define siz(x) (int)(x).size()
#define forall(it,x) for(auto& it:(x))
using namespace __gnu_pbds;
using namespace std;
typedef tree<int, null_type, less<int>, rb_tree_tag,tree_order_statistics_node_update> ordered_set;
//mt19937 mt;void random_start(){mt.seed(chrono::time_point_cast<chrono::milliseconds>(chrono::high_resolution_clock::now()).time_since_epoch().count());}
//ll rand(ll a, ll b) {return a + (mt() % (b-a+1));}
const int INF = 1e9+50;
const ll INF_L = 1e18+40;
const ll MOD = 1e9+7;
struct matrix
{
bool mat[2][2];
matrix()
{
rep(i,2) rep(j,2) mat[i][j] = 0;
}
matrix operator+(const matrix& d)
{
matrix res;
if(mat[0][0] && d.mat[0][0]) res.mat[0][0] = 1;
if(mat[0][1] && d.mat[1][0]) res.mat[0][0] = 1;
if(mat[0][0] && d.mat[0][1]) res.mat[0][1] = 1;
if(mat[0][1] && d.mat[1][1]) res.mat[0][1] = 1;
if(mat[1][0] && d.mat[0][0]) res.mat[1][0] = 1;
if(mat[1][1] && d.mat[1][0]) res.mat[1][0] = 1;
if(mat[1][0] && d.mat[0][1]) res.mat[1][1] = 1;
if(mat[1][1] && d.mat[1][1]) res.mat[1][1] = 1;
return res;
}
};
const int tree_siz = 1024*512-1;
matrix drzewo[tree_siz];
bool is_way()
{
rep(i,2)
{
rep(j,2)
{
if(drzewo[0].mat[i][j]) return true;
}
}
return false;
}
void upd(int v)
{
drzewo[v-1] = drzewo[v*2-1] + drzewo[v*2];
if(v != 1) upd(v/2);
}
pii edges[200'001][2];
bool used[200'001][2];
ld val[200'001][2];
matrix mat[200'001];
void upd_poz(int ind)
{
rep(d1,2) rep(d2,2) mat[ind].mat[d1][d2] = 0;
if(used[ind][0] && edges[ind][0].ff) mat[ind].mat[0][0] = 1;
if(used[ind][0] && edges[ind][0].ss) mat[ind].mat[0][1] = 1;
if(used[ind][1] && edges[ind][1].ff) mat[ind].mat[1][0] = 1;
if(used[ind][1] && edges[ind][1].ss) mat[ind].mat[1][1] = 1;
drzewo[tree_siz/2+ind] = mat[ind];
upd((tree_siz/2+ind+1)/2);
}
int main()
{
ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
//random_start();
rep(i,tree_siz)
{
rep(d1,2) rep(d2,2) drzewo[i].mat[d1][d2] = 1;
}
int n;
cin >> n;
vector<ld> v(n+1);
ld sum = 0;
rep(i,n)
{
cin >> v[i+1];
sum += v[i+1];
}
ld start_mid = sum / (ld)n;
ld pop1 = sum;
pii seg1 = {1,n};
ld pop2 = -1;
pii seg2 = {-1,-1};
val[0][0] = sum/(ld)n;
val[0][1] = -1e9;
rep2(i,1,n-1)
{
if(pop2 == -1)
{
val[i][0] = (sum-v[n]) / (ld)(n-1);
val[i][1] = (sum-v[1]) / (ld)(n-1);
edges[i-1][0] = {1,1};
edges[i-1][1] = {0,0};
pop1 = sum-v[n];
pop2 = sum-v[1];
seg1 = {1,n-1};
seg2 = {2,n};
edges[i][0] = {1,1};
edges[i][1] = {1,1};
// cout << pop1 << " " << pop2 << "\n" << seg1.ff << " " << seg1.ss << "\n" << seg2.ff << " " << seg2.ss << " seg\n\n";
continue;
}
pair<ld,pii> next_L = {-1e16+1,{-1,-1}};
pair<ld,pii> next_R = {+1e16-1,{-1,-1}};
//L
if((pop1 - v[seg1.ss]) / (ld)(n-i) <= start_mid)
{
next_L = max(next_L, {(pop1 - v[seg1.ss]),{seg1.ff,seg1.ss-1}});
}
if((pop2 - v[seg2.ss]) / (ld)(n-i) <= start_mid)
{
next_L = max(next_L, {(pop2 - v[seg2.ss]),{seg2.ff,seg2.ss-1}});
}
//R
if((pop1 - v[seg1.ff]) / (ld)(n-i) >= start_mid)
{
next_R = min(next_R, {(pop1 - v[seg1.ff]),{seg1.ff+1,seg1.ss}});
}
if((pop2 - v[seg2.ff]) / (ld)(n-i) >= start_mid)
{
next_R = min(next_R, {(pop2 - v[seg2.ff]),{seg2.ff+1,seg2.ss}});
}
edges[i-1][0] = {0,0};
edges[i-1][1] = {0,0};
// 0 0
if(seg1.ff == next_L.ss.ff && seg1.ss-1 == next_L.ss.ss)
{
edges[i-1][0].ff = 1;
}
if(seg1.ff+1 == next_L.ss.ff && seg1.ss == next_L.ss.ss)
{
edges[i-1][0].ff = 1;
}
// 0 1
if(seg1.ff + 1 == next_R.ss.ff && seg1.ss == next_R.ss.ss)
{
edges[i-1][0].ss = 1;
}
if(seg1.ff == next_R.ss.ff && seg1.ss -1 == next_R.ss.ss)
{
edges[i-1][0].ss = 1;
}
// 1 0
if(seg2.ff == next_L.ss.ff && seg2.ss-1 == next_L.ss.ss)
{
edges[i-1][1].ff = 1;
}
if(seg2.ff+1 == next_L.ss.ff && seg2.ss == next_L.ss.ss)
{
edges[i-1][1].ff = 1;
}
// 1 1
if(seg2.ff + 1 == next_R.ss.ff && seg2.ss == next_R.ss.ss)
{
edges[i-1][1].ss = 1;
}
if(seg2.ff == next_R.ss.ff && seg2.ss -1 == next_R.ss.ss)
{
edges[i-1][1].ss = 1;
}
val[i][0] = next_L.ff / (ld)(n-i);
val[i][1] = next_R.ff / (ld)(n-i);
pop1 = next_L.ff;
pop2 = next_R.ff;
seg1 = next_L.ss;
seg2 = next_R.ss;
edges[i][0] = {1,1};
edges[i][1] = {1,1};
// cout << pop1 << " " << pop2 << "\n" << seg1.ff << " " << seg1.ss << "\n" << seg2.ff << " " << seg2.ss << " seg\n\n";
}
vector<pair<ld,pii>> points;
rep(i,n)
{
points.pb({val[i][0],{i,0}});
if(i != 0)
{
points.pb({val[i][1],{i,1}});
}
upd_poz(i);
}
sort(all(points));
ld ans = 1e16;
int p = 0;
int k = 0;
while(p < siz(points))
{
if(p != 0)
{
used[points[p-1].ss.ff][points[p-1].ss.ss] = 0;
upd_poz(points[p-1].ss.ff);
}
used[points[p].ss.ff][points[p].ss.ss] = 1;
upd_poz(points[p].ss.ff);
while(!is_way() && k+1 < siz(points))
{
k++;
used[points[k].ss.ff][points[k].ss.ss] = 1;
upd_poz(points[k].ss.ff);
}
// cout << p << " " << k << " " << is_way() << " two\n";
if(is_way())
{
ans = min(ans,points[k].ff-points[p].ff);
}
else break;
p++;
}
cout << setprecision(10) << ans << "\n";
}
