#include<bits/stdc++.h>
#define taskname "A"
using namespace std;
typedef long long ll;
typedef long double ld;
template<class T>void minimize(T& a, T b){
if(a > b){
a = b;
}
}
template<class T>void maximize(T& a, T b){
if(a < b){
a = b;
}
}
const int lim = 2e5 + 5;
int n, a[lim];
ll f[lim];
ld calc(int l, int r){
return ld(f[r] - f[l - 1]) / (r - l + 1);
}
namespace sub1{
void solve(){
ld ans = 1e9;
for(int mask = 0; mask < (1 << (n - 1)); mask++){
int l = 1, r = n;
ld left = 1e9, right = 0;
for(int bit = 0; bit + 1 < n; bit++){
ld x = calc(l, r);
minimize(left, x);
maximize(right, x);
if(mask >> bit & 1){
l++;
}
else{
r--;
}
}
ld x = calc(l, l);
minimize(ans, max(right, x) - min(left, x));
}
cout << setprecision(12) << fixed << ans;
}
}
namespace sub2{
const int lim = 102;
bitset<lim>cur, can[lim];
bool check(){
cur = can[n];
for(int len = n - 1; len > 0; len--){
cur = (cur | (cur << 1)) & can[len];
}
return cur.any();
}
void solve(){
vector<vector<ld>>val(n + 1, vector<ld>(n + 1));
vector<pair<int, int>>range;
for(int l = 1; l <= n; l++){
for(int r = l; r <= n; r++){
range.push_back(make_pair(l, r));
val[l][r] = calc(l, r);
}
}
sort(range.begin(), range.end(), [&] (pair<int, int>i, pair<int, int>j){
return val[i.first][i.second] < val[j.first][j.second];
});
for(int len = n; len > 0; len--){
can[len].reset();
}
ld ans = 1e9;
for(int i = 0, j = 0; i < range.size(); i++){
auto& [l, r] = range[i];
can[r - l + 1][l] = true;
if(check()){
while(true){
auto& [jl, jr] = range[j];
can[jr - jl + 1][jl] = false;
if(!check()){
can[jr - jr + 1][jl] = true;
break;
}
j++;
}
minimize(ans, val[l][r] - val[range[j].first][range[j].second]);
}
}
cout << setprecision(12) << fixed << ans;
}
}
namespace sub3{
void solve(){
vector<vector<ld>>val(n + 1, vector<ld>(n + 1));
vector<pair<int, int>>range;
for(int l = 1; l <= n; l++){
for(int r = l; r <= n; r++){
range.push_back(make_pair(l, r));
val[l][r] = calc(l, r);
}
}
sort(range.begin(), range.end(), [&] (pair<int, int>i, pair<int, int>j){
return val[i.first][i.second] < val[j.first][j.second];
});
vector<int>cnt(n, 0);
ld ans = 1e9;
for(int i = 0, j = 0, cnt_len = 0; i < range.size(); i++){
if(++cnt[range[i].second - range[i].first] == 1){
cnt_len++;
}
while(true){
int len = range[j].second - range[j].first;
if(cnt[len] == 1){
break;
}
cnt[len]--;
j++;
}
if(cnt_len == n){
minimize(ans, val[range[i].first][range[i].second] - val[range[j].first][range[j].second]);
}
}
cout << setprecision(12) << fixed << ans;
}
}
namespace sub4{
void solve(){
ld x = calc(1, n);
vector<pair<ld, int>>val(1, make_pair(x, n));
for(int len = n - 1; len > 0; len--){
int low = 1, high = n - len + 1, p;
while(low <= high){
int mid = (low + high) >> 1;
if(calc(mid, mid + len - 1) <= x){
low = (p = mid) + 1;
}
else{
high = mid - 1;
}
}
val.push_back(make_pair(calc(p, p + len - 1), len));
val.push_back(make_pair(calc(p + 1, p + len), len));
}
sort(val.begin(), val.end());
vector<int>cnt(n + 1, 0);
ld ans = 1e9;
for(int i = 0, j = 0, cnt_len = 0; i < val.size(); i++){
if(++cnt[val[i].second] == 1){
cnt_len++;
}
while(true){
if(cnt[val[j].second] == 1){
break;
}
cnt[val[j++].second]--;
}
if(cnt_len == n){
minimize(ans, val[i].first - val[j].first);
}
}
cout << setprecision(12) << fixed << ans;
}
}
int main(){
ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
if(fopen(taskname".inp", "r")){
freopen(taskname".inp", "r", stdin);
}
cin >> n;
f[0] = 0;
for(int i = 1; i <= n; i++){
cin >> a[i];
f[i] = f[i - 1] + a[i];
}
if(n <= 20){
sub1::solve();
}
else if(n <= 100){
sub2::solve();
}
else if(n <= 2000){
sub3::solve();
}
else{
sub4::solve();
}
}
