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<bits/stdc++.h>
using namespace std;
typedef pair<int,int> p2;
const int N=5e5+5;
const int inf=1e9;
int n;
int h[N],dp[N];
void solvel(int l,int r,int optl,int optr){
if(l>r)return;
int mid=(l+r)/2;
p2 res(-inf,-1);
for(int i=optl;i<=min(mid,optr);i++)res=max(res,p2(h[i]+ceil(sqrt(mid-i))-h[mid],i));
dp[mid]=max(dp[mid],res.first);
int opt=res.second;
solvel(l,mid-1,optl,opt);
solvel(mid+1,r,opt,optr);
}
void solver(int l,int r,int optl,int optr){
if(l>r)return;
int mid=(l+r)/2;
p2 res(-inf,-1);
for(int i=max(mid,optl);i<=optr;i++)res=max(res,p2(h[i]+ceil(sqrt(i-mid))-h[mid],i));
dp[mid]=max(dp[mid],res.first);
int opt=res.second;
solver(l,mid-1,optl,opt);
solver(mid+1,r,opt,optr);
}
int main(){
cin.tie(nullptr)->sync_with_stdio(false);
cin >> n;
for(int i=1;i<=n;i++)cin >> h[i];
solvel(1,n,1,n);
solver(1,n,1,n);
for(int i=1;i<=n;i++)cout << dp[i] << "\n";
}
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