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A. Toda 2

time limit per test

2 secondsmemory limit per test

512 megabytesinput

standard inputoutput

standard outputA 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.

Input

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.

Output

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.

Examples

Input

5

4 5 1 7 4

Output

1

8

01010

00011

01010

10010

00011

11000

00011

11000

Input

2

1 2

Output

0

2

11

11

Input

3

1 1 1

Output

1

0

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