#include<bits/stdc++.h>
using namespace std;
int A[200010];
long long sumy[200010];
struct node{
long double srodek;
int l, r;
bool zapalony;
};
vector<node>tab[200010];
const int base = 1<<18;
bool tree[2*base][2][2];
void update(int x){
x/=2;
while(x>0){
tree[x][0][0] = (tree[x*2][0][0]&tree[x*2+1][0][0])|(tree[x*2][0][1]&tree[x*2+1][1][0]);
tree[x][0][1] = (tree[x*2][0][0]&tree[x*2+1][0][1])|(tree[x*2][0][1]&tree[x*2+1][1][1]);
tree[x][1][0] = (tree[x*2][1][0]&tree[x*2+1][0][0])|(tree[x*2][1][1]&tree[x*2+1][1][0]);
tree[x][1][1] = (tree[x*2][1][0]&tree[x*2+1][0][1])|(tree[x*2][1][1]&tree[x*2+1][1][1]);
x/=2;
}
}
void dodaj(int i, int j){
tab[i][j].zapalony = 1;
auto &ja = tab[i][j];
for(int a=0;a<(int)tab[i-1].size();a++){
auto &pop = tab[i-1][a];
if(abs(pop.l-ja.l)+abs(pop.r-ja.r)==1 && pop.zapalony){
tree[base+i-1][a][j] = 1;
update(base+i-1);
}
}
for(int a=0;a<(int)tab[i+1].size();a++){
auto &pop = tab[i+1][a];
if(abs(pop.l-ja.l)+abs(pop.r-ja.r)==1 && pop.zapalony){
tree[base+i][j][a] = 1;
update(base+i);
}
}
}
void usun(int i, int j){
tab[i][j].zapalony = 0;
auto &ja = tab[i][j];
for(int a=0;a<(int)tab[i-1].size();a++){
auto &pop = tab[i-1][a];
if(abs(pop.l-ja.l)+abs(pop.r-ja.r)==1){
tree[base+i-1][a][j] = 0;
update(base+i-1);
}
}
for(int a=0;a<(int)tab[i+1].size();a++){
auto &pop = tab[i+1][a];
if(abs(pop.l-ja.l)+abs(pop.r-ja.r)==1){
tree[base+i][j][a] = 0;
update(base+i);
}
}
}
vector<vector<bool>>pom;
void zapytaj(int w, int l, int p, int a, int b){
if(l>b || p<a)return;
if(a<=l && p<=b){
pom.push_back({tree[w][0][0], tree[w][0][1], tree[w][1][0], tree[w][1][1]});
return;
}
zapytaj(w*2, l, (l+p)/2, a, b);
zapytaj(w*2+1, (l+p)/2+1, p, a, b);
}
bool Da_sie(int l, int r){
pom.clear();
zapytaj(1, 0, base-1, l, r);
for(int i=1;i<(int)pom.size();i++){
vector<bool>nast={0,0,0,0};
nast[0] = (pom[0][0]&pom[i][0])|(pom[0][1]&pom[i][2]);
nast[1] = (pom[0][0]&pom[i][1])|(pom[0][1]&pom[i][3]);
nast[2] = (pom[0][2]&pom[i][0])|(pom[0][3]&pom[i][2]);
nast[3] = (pom[0][2]&pom[i][1])|(pom[0][3]&pom[i][3]);
pom[0] = nast;
}
return pom[0][0]|pom[0][1]|pom[0][2]|pom[0][3];
}
int main()
{
int n, i;
scanf("%d", &n);
for(i=1;i<=n;i++){
scanf("%d", &A[i]);
sumy[i]=sumy[i-1]+A[i];
}
long double srodek = (long double)sumy[n]/n;
tab[n].push_back({srodek, 1, n});
for(i=n;i>1;i--){
vector<node>kolejna;
for(auto j: tab[i]){
kolejna.push_back({ ((long double)sumy[j.r-1]-sumy[j.l-1])/(j.r-j.l), j.l, j.r-1});
kolejna.push_back({ ((long double)sumy[j.r]-sumy[j.l])/(j.r-j.l), j.l+1, j.r});
}
while(kolejna.size()>=2 && kolejna[kolejna.size()-2].srodek>=srodek)kolejna.pop_back();
reverse(kolejna.begin(), kolejna.end());
while(kolejna.size()>=2 && kolejna[kolejna.size()-2].srodek<=srodek)kolejna.pop_back();
reverse(kolejna.begin(), kolejna.end());
tab[i-1] = kolejna;
}
/*
for(i=1;i<=n;i++){
printf("%d:\n", i);
for(auto j: tab[i])
printf("%Lf %d %d\n", j.srodek, j.l, j.r);
}*/
vector<pair<long double, pair<int,int>>>sorted;
for(i=1;i<=n;i++)
for(int j=0;j<(int)tab[i].size();j++)
sorted.push_back({tab[i][j].srodek, {i, j}});
sort(sorted.begin(), sorted.end());
// for(auto j: sorted)printf("{%Lf %d %d}, ", j.first, j.second.first, j.second.second);printf("\n");
dodaj(sorted[0].second.first, sorted[0].second.second);
int L=0, R=0;
long double wynik = 1000000000;
while(R<(int)sorted.size()){
// printf("L=%d R=%d, %d\n", L, R, (int)Da_sie(0, n-2));
// for(i=0;i<4;i++)printf("%d %d %d %d ", (int)tree[base+i][0][0], (int)tree[base+i][0][1], (int)tree[base+i][1][0], (int)tree[base+i][1][1]);printf("\n");
if(Da_sie(1, n-1)){
wynik = min(wynik, sorted[R].first-sorted[L].first);
usun(sorted[L].second.first, sorted[L].second.second);
L++;
}
else{
R++;
if(R==(int)sorted.size())break;
dodaj(sorted[R].second.first, sorted[R].second.second);
}
}
printf("%Lf\n", wynik);
}
