#include<bits/stdc++.h>

using namespace std;

#define MAXN 100010

const long long INF = 1e15;

int i,n,x;

long long sum[MAXN];

struct point

{

        long long x,y;

} a[MAXN];

inline bool cmpx(point a,point b)

{

        return a.x < b.x;

}

inline bool cmpy(point a,point b)

{

        return a.y < b.y;

}

inline long long dist(point a,point b)

{

        return abs(a.x - b.x) * abs(a.x - b.x) + abs(a.y - b.y) * abs(a.y - b.y);

}

inline long long Closest_Pair(int l,int r)

{

        int i,j,mid,len = ;

        long long d;

        static point s[MAXN];

        if (l == r) return INF;

        if (l +  == r) return dist(a[l],a[r]);

        mid = (l + r) >> ;

        d = min(Closest_Pair(l,mid),Closest_Pair(mid+,r));

        for (i = l; i <= r; i++)

        {

                if ((double)abs(a[i].x - a[mid].x) <= (double)sqrt(d)) s[++len] = a[i];

        }

        sort(s+,s+len+,cmpy);

        for (i = ; i <= len; i++)

        {

                for (j = i + ; j <= len && s[j].y - s[i].y <= sqrt(d); j++)

                {

                        d = min(d,dist(s[i],s[j]));

                }

        }

        return d;

}

int main()

{

        scanf("%d",&n);

        for (i = ; i <= n; i++)

        {

                scanf("%d",&x);

                sum[i] = sum[i-] + x;

        }

        for (i = ; i <= n; i++) a[i] = (point){i,sum[i]};

        sort(a+,a+n+,cmpx);

        printf("%I64d\n",Closest_Pair(,n));

        return ;

}