Toda 2
Contest: 2016-2017 ACM-ICPC, NEERC, Southern Subregional Contest (Online Mirror, ACM-ICPC Rules, Teams Preferred)
Difficulty rating: 1800
Tags: greedy, implementation

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 ri.

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 ri = 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.

Input format:
The first line contains a single integer n (2 ≤ n ≤ 100) — the number of friends.

The second line contains n non-negative integers r1, r2, ..., rn (0 ≤ ri ≤ 100), where ri is the initial rating of the i-th friend.

Output format:
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 104, 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.

Constraints:
Time limit: 2.0 s
Memory limit: 512.0 MB

Example input:
5
4 5 1 7 4

Example output:
1
8
01010
00011
01010
10010
00011
11000
00011
11000

Example input:
2
1 2

Example output:
0
2
11
11

Editorial:
At first we need to decrease two maximum ratings of players until there is exactly one maximum in the array of ratings. It can be easily done: we sort rating in increasing order, take the last and the penultimate ratings, decrease them on one (do not forget, that rating can't became less than 0) and add the information about this decreasing to the answer.
After that we have the array with rating and know that there are at least two maximums. We need to make the following until not all of the rating are the same:
• sort all ratings in increasing order;
• find the number of maximum ratings;
• if this number does not equal to 3, decrease any two maximums on 1 (do not forget, that rating can't became less than 0). In the other case decrease all three maximums on one;
• add the information about decreasing in the answer.
After all ratings became the same we need only to print the answer.