Each of Farmer John's \(N\) cows (\(1\le N\le 2\cdot 10^5\)) has a favorite color.
The cows are conveniently labeled \(1\ldots N\) (as always), and each color can be
represented by an integer in the range \(1\ldots N\).

There exist \(M\) pairs of cows \((a,b)\) such that cow
\(b\) admires cow \(a\) (\(1\le M\le 2\cdot 10^5\)). It is possible that \(a=b\), in which case a cow admires
herself. For any color \(c\), if cows \(x\) and \(y\) both admire a cow with favorite
color \(c\), then \(x\) and \(y\) share the same favorite color.

Given this information, determine an assignment of cows to favorite colors such
that the number of distinct favorite colors among all cows is maximized. As
there are multiple assignments that satisfy this property, output the
lexicographically smallest one (meaning that you should take the assignment that
minimizes the colors assigned to cows \(1\ldots N\) in that order).

Problem credits: William Lin and Benjamin Qi

SCORING

• Test cases 2-3 satisfy \(N,M\le 10^3\).
• Test cases 4-10 satisfy no additional constraints.

Problem credits: William Lin and Benjamin Qi

The first line contains \(N\) and \(M\).

The next \(M\) lines each contain two space-separated integers \(a\) and \(b\)
(\(1\le a,b\le N\)), denoting that cow \(b\) admires cow \(a\). The same pair may
appear more than once in the input.

For each \(i\) in \(1\ldots N\), output the color of cow \(i\) in the desired
assignment on a new line.

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