City Hall

You are the mayor of ICPC City. The city has $N$ intersections, numbered from 1 to $N$. Intersection $i$ has altitude $H_i$. Your house is at intersection $S$, and the city hall is at intersection $T$.

There are $M$ two-way roads, numbered from 1 to $M$. Road $i$ directly connects intersections $U_i$ and $V_i$. Each pair of intersections is directly connected by at most one road. Every intersection can be reached from every other intersection by traversing one or more roads.

Every morning you cycle from your house to the city hall. When you traverse a road connecting intersections $u$ and $v$, the energy you spend is $(H_u - H_v)^2$. The total energy of a path is the sum of the energy spent on each road in that path.

As mayor, you may change the altitude of at most one intersection to any non-negative real number. Using this, you want to minimize the total energy needed to cycle from your house to the city hall.

The first line contains four integers $N$, $M$, $S$, $T$ ($2 \le N \le 100{,}000$; $N-1 \le M \le \min(\frac{N(N-1)}{2}, 200{,}000)$; $1 \le S, T \le N$; $S \ne T$). The next line contains $N$ integers $H_i$ ($0 \le H_i \le 100{,}000$), the altitude of each intersection. Each of the next $M$ lines contains two integers $U_i$ and $V_i$ ($1 \le U_i < V_i \le N$), the intersections joined by road $i$. Each pair of intersections is joined by at most one road, and the roads connect all intersections.

Output one real number on a single line: the minimum total energy. An answer is accepted if its absolute error is at most $10^{-6}$.