This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
//君の手を握ってしまったら
//孤独を知らないこの街には
//もう二度と帰ってくることはできないのでしょう
//君が手を差し伸べた 光で影が生まれる
//歌って聞かせて この話の続き
//連れて行って見たことない星まで
//さユリ - 花の塔
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define int ll
#define starburst ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
#define pii pair<int,int>
#define pb push_back
#define ff first
#define ss second
#define N 100005
void solve(){
int n, s = 0, m1, m2, k; cin >> n;
vector<int> v(n);
for(auto &x:v) cin >> x, s += x;
double bary = (double) s / (double) n, l, r, ans = 1e9;
l = r = bary;
m1 = v[n / 2], m2 = v[(n - 1) / 2];
k = n;
int he = 0, ta = n - 1, tmp = s;
while(he != ta){
if(bary < m1){
tmp -= v[he]; he++; --k;
bary = (double)tmp / (double)k;
r = max(r, bary);
}else if(bary > m1){
tmp -= v[ta]; ta--; --k;
bary = (double)tmp / (double)k;
l = min(l, bary);
}else{
if(abs(m1 - v[he]) >= abs(m1 - v[ta])){
s -= v[he]; he++; --k;
bary = (double)tmp / (double)k;
r = max(r, bary);
}else{
tmp -= v[ta]; ta--; --k;
bary = (double)tmp / (double)k;
l = min(l, bary);
}
}
}
ans = min(ans, r - l);
k = n;
he = 0, ta = n - 1;
tmp = s;
bary = (double) s / (double) n;
l = r = bary;
while(he != ta){
if(bary < m2){
tmp -= v[he]; he++; --k;
bary = (double)tmp / (double)k;
r = max(r, bary);
}else if(bary > m2){
tmp -= v[ta]; ta--; --k;
bary = (double)tmp / (double)k;
l = min(l, bary);
}else{
if(abs(m2 - v[he]) >= abs(m2 - v[ta])){
s -= v[he]; he++; --k;
bary = (double)tmp / (double)k;
r = max(r, bary);
}else{
tmp -= v[ta]; ta--; --k;
bary = (double)tmp / (double)k;
l = min(l, bary);
}
}
}
ans = min(ans, r - l);
cout << fixed << setprecision(9) << ans << '\n';
}
signed main(){
starburst
int t = 1; //cin >> t;
while(t--) solve();
}
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