Toda 2

有N个人打 Toda 2（Dota 2）.他们希望通过某种方法使得他们的rating一致。为了让rating一致，他们可以组成 2-5人的队，并且主动输掉这场比赛来掉1分。 rating不能为负。 给你这N个朋友的初始rating （N<100, R<100)，求他们该如何组队掉分，才能让最后rating一致，且此 rating要尽可能的大。 输出 第一行为最终 rating，第二行是游戏场数，后面每行一个01串，表示每次有哪些人参与了游戏（0,1代表是否参加）。 感谢@chengni 提供的翻译

A group of $ n $ friends enjoys playing popular video game Toda 2. There is a rating system describing skill level of each player, initially the rating of the $ i $ -th friend is $ r_{i} $ . The friends decided to take part in the championship as a team. But they should have equal ratings to be allowed to compose a single team consisting of all $ n $ friends. So the friends are faced with the problem: how to make all their ratings equal. One way to change ratings is to willingly lose in some matches. Friends can form a party consisting of two to five (but not more than $ n $ ) friends and play a match in the game. When the party loses, the rating of each of its members decreases by $ 1 $ . A rating can't become negative, so $ r_{i}=0 $ doesn't change after losing. The friends can take part in multiple matches, each time making a party from any subset of friends (but remember about constraints on party size: from $ 2 $ to $ 5 $ members). The friends want to make their ratings equal but as high as possible. Help the friends develop a strategy of losing the matches so that all their ratings become equal and the resulting rating is maximum possible.

The first line contains a single integer $ n $ ( $ 2<=n<=100 $ ) — the number of friends. The second line contains $ n $ non-negative integers $ r_{1},r_{2},...,r_{n} $ ( $ 0<=r_{i}<=100 $ ), where $ r_{i} $ is the initial rating of the $ i $ -th friend.

In the first line, print a single integer $ R $ — the final rating of each of the friends. In the second line, print integer $ t $ — the number of matches the friends have to play. Each of the following $ t $ lines should contain $ n $ characters '0' or '1', where the $ j $ -th character of the $ i $ -th line is equal to: - '0', if friend $ j $ should not play in match $ i $ , - '1', if friend $ j $ should play in match $ i $ . Each line should contain between two and five characters '1', inclusive. The value $ t $ should not exceed $ 10^{4} $ , it is guaranteed that such solution exists. Remember that you shouldn't minimize the value $ t $ , but you should maximize $ R $ . If there are multiple solutions, print any of them.

5
4 5 1 7 4

1
8
01010
00011
01010
10010
00011
11000
00011
11000

2
1 2

0
2
11
11

3
1 1 1

1
0