Beautiful League

Description:

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.

Sample Input:

3 1
1 2

Sample Output:

010
001
100

Sample Input:

4 2
1 2
1 3

Sample 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: $$$(1, 2, 4)$$$, $$$(2, 4, 1)$$$, $$$(4, 1, 2)$$$, $$$(2, 4, 3)$$$, $$$(4, 3, 2)$$$, $$$(3, 2, 4)$$$.