Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

The problem statement has recently been changed. View the changes.

×
E. Beautiful League

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputA football league has recently begun in Beautiful land. There are $$$n$$$ teams participating in the league. Let's enumerate them with integers from $$$1$$$ to $$$n$$$.

There will be played exactly $$$\frac{n(n-1)}{2}$$$ matches: each team will play against all other teams exactly once. In each match, there is always a winner and loser and there is no draw.

After all matches are played, the organizers will count the number of beautiful triples. Let's call a triple of three teams $$$(A, B, C)$$$ beautiful if a team $$$A$$$ win against a team $$$B$$$, a team $$$B$$$ win against a team $$$C$$$ and a team $$$C$$$ win against a team $$$A$$$. We look only to a triples of different teams and the order of teams in the triple is important.

The beauty of the league is the number of beautiful triples.

At the moment, $$$m$$$ matches were played and their results are known.

What is the maximum beauty of the league that can be, after playing all remaining matches? Also find a possible results for all remaining $$$\frac{n(n-1)}{2} - m$$$ matches, so that the league has this maximum beauty.

Input

The first line contains two integers $$$n, m$$$ ($$$3 \leq n \leq 50, 0 \leq m \leq \frac{n(n-1)}{2}$$$) — the number of teams in the football league and the number of matches that were played.

Each of $$$m$$$ following lines contains two integers $$$u$$$ and $$$v$$$ ($$$1 \leq u, v \leq n$$$, $$$u \neq v$$$) denoting that the $$$u$$$-th team won against the $$$v$$$-th team. It is guaranteed that each unordered pair of teams appears at most once.

Output

Print $$$n$$$ lines, each line having a string of exactly $$$n$$$ characters. Each character must be either $$$0$$$ or $$$1$$$.

Let $$$a_{ij}$$$ be the $$$j$$$-th number in the $$$i$$$-th line. For all $$$1 \leq i \leq n$$$ it should be true, that $$$a_{ii} = 0$$$. For all pairs of teams $$$i \neq j$$$ the number $$$a_{ij}$$$ indicates the result of the match between the $$$i$$$-th team and the $$$j$$$-th team:

- If $$$a_{ij}$$$ is $$$1$$$, the $$$i$$$-th team wins against the $$$j$$$-th team;
- Otherwise the $$$j$$$-th team wins against the $$$i$$$-th team;
- Also, it should be true, that $$$a_{ij} + a_{ji} = 1$$$.

Also note that the results of the $$$m$$$ matches that were already played cannot be changed in your league.

The beauty of the league in the output should be maximum possible. If there are multiple possible answers with maximum beauty, you can print any of them.

Examples

Input

3 1 1 2

Output

010 001 100

Input

4 2 1 2 1 3

Output

0110 0001 0100 1010

Note

The beauty of league in the first test case is equal to $$$3$$$ because there exists three beautiful triples: $$$(1, 2, 3)$$$, $$$(2, 3, 1)$$$, $$$(3, 1, 2)$$$.

The beauty of league in the second test is equal to $$$6$$$ because there exists six beautiful triples: $$$(1, 2, 4)$$$, $$$(2, 4, 1)$$$, $$$(4, 1, 2)$$$, $$$(2, 4, 3)$$$, $$$(4, 3, 2)$$$, $$$(3, 2, 4)$$$.

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Jun/18/2021 14:22:40 (g2).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|