CF 429D

#include<cstdio>
#include<cstdlib>
#include<algorithm>
#include<cmath>
#include<cstring>
#include<utility>
#define x first
#define y second

using namespace std;

typedef long long ll;

typedef pair<ll,ll> pi;

pi a[100011],ts[100011],que[100011];
int n,i,x;
ll ans,pre[100011];

ll dis(pi a,pi b)
{
    return (a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y);
}

bool cmpy(pi a,pi b)
{
    return a.y<b.y;
}

void Solve(int l,int r)
{
    int tc,mid,L,R,i,j;
    ll mx;
    if(l+1>=r){
        if(r==l+1)ans=min(ans,dis(a[l],a[r]));
        return;
    }
    mid=(l+r)/2;
    Solve(l,mid);
    Solve(mid+1,r);
    mx=a[mid].x;
    tc=0;
    for(i=mid;i>=l;i--){
        if((mx-a[i].x)*(mx-a[i].x)>=ans)break;
        ts[++tc]=a[i];
    }
    for(i=mid+1;i<=r;i++){
        if((mx-a[i].x)*(mx-a[i].x)>=ans)break;
        ts[++tc]=a[i];
    }
    sort(ts+1,ts+1+tc,cmpy);
    L=1;R=0;
    for(i=1;i<=tc;i++){
        R++;
        que[R]=ts[i];
        while(L<R&&(que[L].y-que[R].y)*(que[L].y-que[R].y)>=ans)L++;
        for(j=L;j<R;j++)ans=min(ans,dis(que[j],que[R]));
    }
    
}

int main()
{
    scanf("%d",&n);
    for(i=1;i<=n;i++){
        scanf("%d",&x);
        pre[i]=pre[i-1]+x;
        a[i].x=i;a[i].y=pre[i];
    }
    ans=1ll<<60;
    Solve(1,n);
    printf("%I64d\n",ans);
}