Tourist Petr

Vera met Petr, a friendly volleyball player and tractor driver, while on vacation in a Warm Country. Petr, a tourist, plans to travel through European cities after the vacation. Europe has a well-developed transport system. There are $V$ cities that interest Petr and $E$ night train routes. Each route connects two different cities, and the trip takes one night. Trains run in both directions.

Petr wants the whole trip to take no more than four days. He spends exactly one day sightseeing in each city, and he spends each night on a night train between cities. Petr does not want to visit any city more than once.

For each city, Petr has estimated his expected enjoyment $p_i$ of visiting it. Find a route that gives Petr the greatest total enjoyment.

The first line contains two integers $V$ and $E$ ($1 \le V, E \le 3 \times 10^5$), the number of cities and the number of train routes.

The second line contains $V$ integers $p_1, p_2, \ldots, p_V$ ($1 \le p_i \le 10^8$), where $p_i$ is the expected enjoyment of visiting city $i$.

Each of the next $E$ lines describes a route with two different integers $a_i$ and $b_i$ ($1 \le a_i, b_i \le V$), the numbers of the cities that the route connects. There is at most one route between any pair of cities.

On the first line, print the number $K$ of cities on the optimal route ($1 \le K \le 4$). On the second line, print the numbers of these cities in the order of the visit. Cities are numbered starting from 1. If several optimal routes exist, print any of them.