You are given a permutation of the numbers 1,2,...,n and m pairs of positions (aj,bj).
At each step you can choose a pair from the given positions and swap the numbers in that positions. What is the lexicographically maximal permutation one can get?
Let p and q be two permutations of the numbers 1,2,...,n. p is lexicographically smaller than the q if a number 1≤i≤n exists, so pk=qk for 1≤k<i and pi<qi.
The first line contains two integers n and m (1≤n,m≤106) − the length of the permutation p and the number of pairs of positions.
The second line contains n distinct integers pi (1≤pi≤n) − the elements of the permutation p.
Each of the last m lines contains two integers (aj,bj) (1≤aj,bj≤n) − the pairs of positions to swap. Note that you are given a positions, not the values to swap.
Print the only line with n distinct integers p'i (1≤p'i≤n) − the lexicographically maximal permutation one can get.
9 6
1 2 3 4 5 6 7 8 9
1 4
4 7
2 5
5 8
3 6
6 9
7 8 9 4 5 6 1 2 3