This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <algorithm>
#include <iostream>
#include <numeric>
#include <iomanip>
#include <cassert>
#include <vector>
#include <queue>
#include <set>
typedef long long llong;
const int MAXN = 200000 + 10;
const int INF = 2e9;
int n;
int a[MAXN];
llong prefix[MAXN];
long double calc(int l, int r)
{
return ((long double)(prefix[r] - prefix[l - 1])) / (r - l + 1);
}
long double check(long double from)
{
long double to = from;
int l = 1, r = n;
while (true)
{
to = std::max(to, calc(l, r));
if (l == r)
{
break;
}
if (calc(l, r - 1) > from)
{
r--;
} else
{
l++;
}
}
return to - from;
}
void solve()
{
for (int i = 1 ; i <= n ; ++i)
{
prefix[i] = prefix[i - 1] + a[i];
}
long double l = 0.0, r = calc(1, n), midL, midR;
for (int i = 0 ; i < 100 ; ++i)
{
midL = l + (r - l) / 3.0;
midR = l + 2 * (r - l) / 3.0;
if (check(midL) < check(midR)) r = midR;
else l = midL;
}
std::cout << std::fixed << std::setprecision(10) << check(l) << '\n';
}
void input()
{
std::cin >> n;
for (int i = 1 ; i <= n ; ++i)
{
std::cin >> a[i];
}
}
void fastIOI()
{
std::ios_base :: sync_with_stdio(0);
std::cout.tie(nullptr);
std::cin.tie(nullptr);
}
int main()
{
fastIOI();
input();
solve();
return 0;
}
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