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).

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

#4169 upload 7 done 2 how_to_reg 2

Favorite Colors timer 1s memory 512MB

#4169

Favorite Colors 1s 512MB