Popularity Contest

*It’s not about what you know, but who you know*. A
famous saying – but is it true? You start looking around
yourself, pondering what lies behind the success of some of
your friends. Could it be that life is just one big popularity
contest? Are all the hours you spend learning algorithms better
used networking?

Slightly saddened by these thoughts, you realize that this
is at least a question you can answer thanks to all those
algorithm hours. Among your $N$ friends, $M$ pairs of them are friends with
each other. You have ordered your friends in increasing order
by how successful you think they are in life. For the
$i$’th friend (starting
from $1$) in this order,
we let $i$ be their
*success factor*. Similarly, we call the number of
friends someone has their *popularity factor*
$P_ i$.

To investigate the matter, you decide to compute the
*marketability coefficient* of each friend, defined as
the difference between their popularity factor and success
factor.

The first line contains an integer $N$ ($2 \le N \le 1\, 000$), the number of your friends, and $M$ ($0 \le M \le \frac{N(N - 1)}{2}$), the number of friendships.

The next $M$ lines each contains one of the friendships, given as two integers $1 \le a \neq b \le N$, denoting that the $a$’th and $b$’th of your friends are friends.

Output a single line with $N$ integers – the marketability coefficients of all your friends.

Sample Input 1 | Sample Output 1 |
---|---|

4 0 |
-1 -2 -3 -4 |

Sample Input 2 | Sample Output 2 |
---|---|

4 3 2 1 1 4 2 3 |
1 0 -2 -3 |