Let's Split Up!

As every horror movie shows, sooner or later someone comes up with the brilliant idea of splitting up to explore a creepy, suspicious place in small groups.

This time a party of $n + 2$ people is exploring an abandoned hut in a dark forest, and they decide to split into two groups. The party has two leaders with recklessness $a_1$ and $a_2$. Two rooms are available for the search, with suspicion levels $b_1$ and $b_2$.

Each group must have exactly one of the two leaders. If the group of the $i$-th leader has $k_i$ people (not counting the leader) and explores room $j$, the danger of that search is $D = a_i \cdot k_i \cdot b_j$.

You want to help them minimize the danger of this plan. Split the $n$ non-leaders into two groups (one group may be empty), and assign each group a leader and a room so that the larger of the two dangers is as small as possible.

The first line contains one integer $n$, the number of people not counting the two leaders ($1 \leqslant n \leqslant 10^9$).

The second line contains two integers $a_1$ and $a_2$, the recklessness levels of the two leaders ($1 \leqslant a_1, a_2 \leqslant 10^4$).

The third line contains two integers $b_1$ and $b_2$, the suspicion levels of the rooms ($1 \leqslant b_1, b_2 \leqslant 10^4$).

Print one integer, the smallest possible value of the larger of the two dangers.

On the next line, print the number of the room that the first leader's group explores and the number of people in that group (not counting the leader), separated by a space. On the last line, print the same information for the second leader's group.

If there are several answers, print any of them.