#include <bits/stdc++.h>
#include <bits/extc++.h>
#define StarBurstStream ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0);
#define iter(a) a.begin(), a.end()
#define riter(a) a.rbegin(), a.rend()
#define lsort(a) sort(iter(a))
#define gsort(a) sort(riter(a))
#define pb(a) push_back(a)
#define eb(a) emplace_back(a)
#define pf(a) push_front(a)
#define ef(a) emplace_front(a)
#define pob pop_back()
#define pof pop_front()
#define mp(a, b) make_pair(a, b)
#define F first
#define S second
#define mt make_tuple
#define gt(t, i) get<i>(t)
#define tomax(a, b) ((a) = max((a), (b)))
#define tomin(a, b) ((a) = min((a), (b)))
#define topos(a) ((a) = (((a) % MOD + MOD) % MOD))
#define uni(a) a.resize(unique(iter(a)) - a.begin())
#define printv(a, b) {bool pvaspace=false; \
for(auto pva : a){ \
if(pvaspace) b << " "; pvaspace=true;\
b << pva;\
}\
b << "\n";}
using namespace std;
using namespace __gnu_pbds;
typedef long long ll;
typedef unsigned long long ull;
typedef long double ld;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using pdd = pair<ld, ld>;
using tiii = tuple<int, int, int>;
const ll MOD = 1000000007;
const ll MAX = 2147483647;
template<typename A, typename B>
ostream& operator<<(ostream& o, pair<A, B> p){
return o << '(' << p.F << ',' << p.S << ')';
}
ll ifloor(ll a, ll b){
if(b < 0) a *= -1, b *= -1;
if(a < 0) return (a - b + 1) / b;
else return a / b;
}
ll iceil(ll a, ll b){
if(b < 0) a *= -1, b *= -1;
if(a > 0) return (a + b - 1) / b;
else return a / b;
}
struct Comp{
bool operator()(pll xc, pll yc){
return (__int128)xc.F * yc.S < (__int128)yc.F * xc.S;
}
};
void waassert(bool t){
if(t) return;
cout << "WA\n";
exit(0);
}
int main(){
StarBurstStream
int n;
cin >> n;
vector<ll> a(n + 1), s(n + 1);
for(int i = 1; i <= n; i++) cin >> a[i], s[i] = s[i - 1] + a[i];
auto getcen = [&](int l, int r){
return mp(s[r] - s[l - 1], r - l + 1);
};
auto comp = [&](pll xc, pll yc){
return (__int128)xc.F * yc.S < (__int128)yc.F * xc.S;
};
auto getdis = [&](pll x, pll y){
ld tx = (ld)x.F / x.S;
ld ty = (ld)y.F / y.S;
return abs(tx - ty);
};
pll mid = getcen(1, n);
vector<pii> good;
vector<pii> lg(n + 1), rg(n + 1);
lg[n] = rg[n] = mp(1, n);
for(int i = 0; i < n - 1; i++){
{
int l = 1, r = n - i;
while(l < r){
int m = (l + r) / 2;
if(comp(getcen(m, m + i), mid)) l = m + 1;
else r = m;
}
rg[i + 1] = mp(l, l + i);
}
{
int l = 1, r = n - i;
while(l < r){
int m = (l + r + 1) / 2;
if(comp(mid, getcen(m, m + i))) r = m - 1;
else l = m;
}
good.eb(mp(l, l + i));
lg[i + 1] = mp(l, l + i);
}
}
/*printv(lg, cerr);
printv(rg, cerr);*/
sort(iter(good), [&](pii x, pii y){ return comp(getcen(x.F, x.S), getcen(y.F, y.S)); });
reverse(iter(good));
multiset<pll, Comp> st;
for(int i = 1; i <= n; i++){
st.insert(getcen(rg[i].F, rg[i].S));
}
ld ans = getdis(*st.begin(), *st.rbegin());
/*cerr << "test ";
printv(st, cerr);*/
for(pll i : good){
int len = i.S - i.F + 1;
auto it = st.find(getcen(rg[len].F, rg[len].S));
st.erase(it);
st.insert(getcen(i.F, i.S));
/*cerr << "test " << i << " : ";
printv(st, cerr);*/
ans = min(ans, getdis(*st.begin(), *st.rbegin()));
}
cout << fixed << setprecision(20) << ans << "\n";
return 0;
}
