A10600. Toda 2

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.